I think that's taking the analogy of a fork a bit too far - typically the express purpose of a token smart contract includes the person-to-person transfer. It's a token therefore it can be traded/transferred like a token.

But the contract isn't typically written to blockchain-fork. If it were some game or MLM it might be written in that fashion - to fork at some arbitrary event. But then it should be part of the source code to take in that event and to the fork. There have been some contracts that have done similar things.

In contrast, what I'm worried about is things outside the contract that cause the contract to in effect fork. If the contract has to be written with that in mind, it's a weakness - yet another trap for contract writers to worry about. If the chain encourages that, it effects potentially all contracts... for hypothetical example, on Ethereum, do contracts need a certification that they are fork-safe?