The hardest possible target is all zeros plus a one (0000000...1). If such a block were ever mined (which is extremely unlikely: on average you’d need 2^255 hashes per 10 minutes, which is 9.6e73 hashes per second), it would definitely crash the network : there can only be one hash at that difficulty, which means that there can only be one block mined at that difficulty.
Of course, if the target is zero, no block can be mined at all.
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