Usually it will either will rip the tape, or break the print somehow. Currently using ABS on a taped glass bed with a layer of hairspray for adhesion.
I moved to a plain glass heated bed with a brush applied acetone and ABS mixture. Using an old emptied nail polish bottle with brush, I added some acetone and then threw in ABS pieces until it reached a brush-able consistency. I then brush it on the glass build plate where I believe the print will occur, and it works very well. On removal of the part the coating comes with it.
I just found previously that ABS would adhere to my kapton taped heated bed too strongly to use, and so while this involves a little work before each print, it's overall better than kapton for me.
I did experiment with sheet metal beds coated with kapton, but they curl during printing due to the ABS thermal stress, allowing my parts to be concave on the bottom side. Easy to remove from the plate, though, since it flexed. There may be a good middle ground material but I didn't experiment further.
Glass has a very peculiar effect under heating, that can be used to remove extremely delicate parts from the surface of it:
Glass expands and shrinks differently to the ABS under temperature. Letting the glass bed cool down has it shrink, creating tension on the interface layer which can be exploited with a thin scraper. Putting the bed with the print into the fridge increases the tension to a point at which the bonding breaks. This results in the part popping free in several areas (sometimes everywhere) and easing the removal.