There's a couple of ways you can tell, one is if it's oxidized and there'll
be actual rust on the string, that generally means that it's time to put
new ones on there. If they look okay and they feel okay, a lot of times
when the cores of the strings start to go bad they won't stay in tune
anymore and you can tell that by checking to see if the bass is playing in
tune by playing into a tuner.
Some people like stings, on a bass
especially, to be very old and they'll play them for as long as they
possibly can, I've known guys that kept them on there for a number of years
at a time. Some guys like them to be really new because if they're new
they're really bright and punchy. I like strings to be warm and kind of
older so I try to take it to the max. Generally the bass strings really
won't break unless you're a very, very aggressive player but most dudes
don't do that.
If you're trying to intonate the bass to get it to play in
tune with itself and it will not do it, it generally means that the core of
the string itself, it's usually a solid piece of steel with one string on
top of that, the core of that has started to corrode. When you pluck it,
the string will not play in tune anymore. Usually they start to corrode on
the outside before that happens and you just don't want to play rusty
strings, they don't sound good they cause fret flies and stuff like that.