Fortunately there is a limit: the universe (in a practical sense). You cannot encode all states it has in a hash as it would require more states than you want to encode as you already mentioned (pigeon hole). But representing macroscopic data like text (or basically anything bigger than atomic scale) uniquely can be done with 128+ bits. Double that and you are likely safe for collisions, assuming the method you use is uniform and not biased to some input.

If you want ease collision examples you can take a look at people using CRC32 as hashes/digests. It is notoriously prone to collisions (since only 32 bits).