Jeff Liebermann wrote:

What if a portion of the EPROM stays unprogrammed ('FF') and the
chip goes through some program-erase cycles? The unprogrammed area
should fail sooner or later, shouldn't it?

It's a bad EPROM. If the blank check on your unspecified EPROM burner
says it's not blank, it's not blank.

I meant another thing: what will happen if a chip undergoes several
write/erase cycles where an area is intentionally left unprogrammed
every time? It's like erasing it over and over.
Probably nothing, I think. It must have happened quite often that some
byte (or bit, why not?) would always be unprogrammed at every cycle in
the prototyping process, so it shouln't be a problem.