hashCode() for string returning negative value

Are negative values expected for hashCode()?

They're entirely valid, yes.

won't the value keep increasing as the length of string increase and eventually be greater than Integer.MAX_VALUE?

What makes you think that hash codes increase as the length of the string increases?

Basically, you should think of hash codes as fingerprints - collections of bits rather than numbers with a meaningful magnitude. Hash code calculations very often overflow or underflow, and that's absolutely fine. "More" or "less" are irrelevant comparisons between hash codes - all that's relevant is "equal" or "not equal", where the rules are that the hash codes for two equal values must be equal, but the hash codes for two non-equal values may still be equal. The numeric values are relevant in terms of bucketing, but that's usually an implementation detail of whatever's using them.

A hash code is just a quick way of finding values which are definitely not equal. So consider a situation where I have a set of strings with hash codes { 1, -15, 20, 5, 100 }. If I'm given a string with a hash code of 14, I know that string definitely isn't in the set. If I'm given a string with a hash code of 20, I need to check it with equals against the string in my set with a hash code of 20, to see whether or not the candidate string is in the set.