Avoiding potential "hang-ups"
Many people don’t put collars on their cats, especially if those cats are exclusively indoors. Unfortunately, even “indoor-only” cats will occasionally get out.
There’s little debate that identifying your cat — ideally with both a collar/tag and a microchip — is your best bet for getting your cat back should they ever become lost. (A possibility that’s sadly even more likely to happen with the upcoming fireworks on and around the 4th of July!)
For many people their reason for not putting a collar and tag on, even on their outdoor cats, is the fear that their cat could get their collar caught on a fence, tree branch, or something else and become stranded or strangled in the process. While this is an understandable and realistic fear, fortunately these scenarios seem to happen relatively infrequently (at least as far as we know). That said, when such events do happen, they can do so with devastating and heart-breaking consequences.
To help keep your cats identifiable and safe I’d recommend looking into and using a well-fitted and reliable break-away style collar — an option that many cat owners aren’t even aware of.
Break-Away Collars For Cats

There are several brands on the market (incl. National Leash, Lupine Pet, and others) so be sure to test how easy or hard it is to get the collar clasp to actually break-away by comparing how much stretch and pressure you have to exert to get it to release. You'll want to approximate which level of release would be best for your cat based on their size and weight.
These types of collars can save lives, so they’re definitely worth checking out. But since they are designed to come off in dangerous situations, don’t forget about the importance of also microchipping (and of periodically ensuring that your contact information associated with that microchip is current).