The Illustrator path eraser tool can be found in the toolbar beneath the shaper (it is tucked away). It has no options, you simply apply it to the selected lines and the parts of that line will be removed. It only removes the part of the segment it passes over. You have to use the rubber part of the cursor to cut away the line, it is no use using the start point - that is key. You may just end up scratching your head wondering why it doesn't work, the rubber is KEY!
Select a rectangle / circle / star etc and add a stroke to it say of 20pt and then select it and use the rubber over part of the top part of the line and from the start point to the end point release of the mouse, the line will be removed and you will now have an open line for your rectangle, you will still see any fill applied but it will be split across the two or more filled designs. You can repeat this cutting action and generate multiple grouped lines and you will see the fill change to reflect the new lines created.
The lines are all now separate and, if selected, can also be cut by the rubber. Simply hover of the start point for your cut and the end point of your cut. You can color the lines using the swatches panel and select a new fill etc for each curve or line you have (if you select all the lines and you have the powerful plugin called Randomino, you can now change all the colors in one go as well as apply random scale, rotation etc)
Of course it does not need to be just applied to a square / circle etc but all kinds of lines can be cut using this technique such as complex designs created using the anchor or curvature etc as well as ones modified by effect such as zigzag lines
Select any of the lines, apply the rubber and break apart the design / remove parts of the curve / line (as little or as much as you require). You can also select all the now open and apply a width profile via the properties panel or when using the selection, there are a small selection of profiles to be applied. You can also use the width brush and manipulate the open lines to make them more like pen strokes or bulge or shrink along the line. If there was a width profile before you split / remove parts of the line, the width profile is now applied to the new open ones.
Select a line with a complex set of fills and strokes etc and go to the appearance panel and you see the break down of the strokes etc. You can also use it and apply over parts of that and the lines will be broken down into smaller fragments of lines with the same appearance
You can also apply it to brush strokes. Apply a brush and then apply it to cut the brush strokes into fragments. The end result can be far more intense brush strokes all with the same settings
Select a line or curve etc and go to the object menu and repeat and radial (or grid or mirror). You will now see a repeat object, you cannot split this, if you try, it will just be ignored. You need to go to selection, double click one of the instances in the repeat object and you will find yourself in the editing mode for that object (to exit, just right click and select the exit command or use the breadcrumbs in the top left of the control bar). You can now cut or remove parts of the line / curve and any change you make to the main editing instance will be reflected in all the other instances in the repeat. You can then select the open lines / curves and move them and rotate them and distort them as normal and each one will be updated. You can then again remove more of the design etc as required. Exit from this by right clicking and selecting the exit command. You can now see the result of the changes made and you can now increase the number of these instances and also modify the radius. You can also use the expand to just them as normal editable lines / curves again.
You can create a quick jagged line by using it. Use the Line segment and create a straight line by holding down the shift key and drawing from left to right or top to bottom. Keep selected. Use the rubber to create very tiny marks over the line. You may find it easier to use the zoom feature to really zoom into the artwork and create very subtle rubbing actions to remove a small part of the curve (not sure if there is a defined minimum that can be removed). Unfortunately, if you want to go back and remove more of a previous line, you have to re-select it. You can repeat this action over and over until your line has 20 or 30 small slices into it and you can select them individually and move them up or down or re-color them perhaps with subtle variations of the original color. You can also use a powerful plugin called Randomino and that can re-color, position, scale etc in random ways all the lines selected. Another useful feature would be the transform each command found in the object menu with the items selected and use the scale, etc there and also set random ON to create a very jagged line
You can always turn the stroke designs into fills by using the object menu and expand command and you will then have a selection of closed fill and stroke designs to work with the rubber.
You can also use the rubber with a warped line. Select a line or any design and then apply a warp to it via the object menu and envelope distort and warp. You can then edit the contents of that line to create truly weird and wonderful warps. It is quite odd to see the warping re-applied as soon as you use the rubber to any curve / line. You cannot rub away the warp though.
You can create all kinds of very long curved doodle like curves with the curvature feature. You can then cut it. Apply it along the selected curve, say in the middle of the doodle and run the rubber along part of that and it will vanish, you will still have the rest of the doodle. It was an open curve before applying the rubber but it will now be two curves instead, As you apply the rubber along the curve, the last used curve will still be selected but as soon as you apply the rubber again the curve will be deselected (there is no keep everything selected feature with the rubber which is a pity as that would be a super handy preference to have). You have to use the good old cmd or ctrl A to re-select everything or use the selection. You can then again apply the rubber to the curve breaking it apart more and more until it becomes fragments. Each of those curves are now separate and can be re-colored etc and widths changed and more.
The rubber does not work on type etc unless expanded. Select some type, check spelling and then object menu and expand. Ungroup via the object menu. Select a character and cut the design or remove parts of the object. Again, select all is super useful here as it only works on selected lines. Once you have done this you have your broken type. You can now select the individual parts. Or perhaps object menu and ungroup and then perhaps use the object menu and transform and transform each with random setting ON and scale and transform the design. You can also then select all the type and object menu and expand to turn them into filled designs and use the same object menu transform each mixing with re-colored designs and more. You can also double click the individual parts of the characters and enter isolation mode and then shift the individual fragmented parts of the type. You can also release the entire type set from being compound by going to the object menu and compound and release and then you will be able to re-color the entire design or use the live paint bucket fill to fill the selected shapes of the type with different colors. After expanding the live paint bucket color changes, you can also go to the object menu and ungroup (you may have to do this a few times) and then you will (finally) have separate character fragments that can be modified further using transforms such as transform each with random.