Can cells get burned in EPROM by programming twice?
The MC27C256 and similar UV EPROM cells are at a logic '1' when bulk erased by exposure to UV light, and a cell can be electrically written to a logic '0'. Re-writing a cell that is already '0' to another '0' has no effect, and attempting to re-write a '0' cell to a '1' will be unsuccessful. Once a cell has been set to logic '0' it remains '0' until the entire EPROM is erased to all '1's.

By the way, the same silicon chip that is in the UV EPROM may also be sold at a lower price in plastic package as OTP (One Time Programmable); it's the same chip except it can't be erased because of the lower-cost packaging. The little window on the top of the UV EPROM package is made of quartz crystal, and it has to be encased in a package that has the same temperature coefficient of expansion, so plastic is out and metal is out, it has to be ceramic. The cost difference is significant.

Back in the day, we used UV EEPROMs for firmware development, and once the firmware was pretty stable we'd switch to the cheaper OTP for building up a larger batch of prototypes or building production boards.

The normal cycle involved plugging the EPROM into a device programmer to write the memory image, then cover the window with an opaque removable paper label (both to identify the firmware version and protect against stray UV light possibly eroding the image). Then unplug from the device programmer and plug into the target board for testing. More changes needed? Then put another EPROM into the device programmer, write image, label it, unplug the old EPROM and plug in the new EPROM into the target board. Then scrape off the sticky label from the old EPROM, clean off the window, and put it in the UV eraser like stacking dirty dishes in the dishwasher, until there are enough to run a full cycle. The UV bulb has a limited lifetime, so you want to erase as many EPROMs as you can with each 20 minute cycle.

All this changed for the better once Electrically Erasable (EEPROM) became widely available; no more need to pull EPROMs from the sockets and bake for 20 minutes in the UV eraser bin. Eliminated the need for the UV bulbs, the sockets themselves and the plugging and unplugging, so developers were willing to pay a premium for EEPROM.