However, if you are only forking the vm and allowing for people de deploy other protocols (or forks of other protocols), this is not the case (they just start off at lower total supply relative to the native collateral available on that network from a lower demand base).
I think id agree for things like ZCash/Dash etc compared to BTC, but I'm not sure I'd agree when it comes to the all contracts deployed on all EVM networks and none of this has anything to do with decentralized stablecoins.
For example, you can mint MIM (a decentralized stablecoin) on both avalanche c-chain and ethereum (as well as polygon, fantom, bsc and arbitrum), and they are both worth $1, but have different collateral backing it on both networks. If users wanted to leave one or the other, they could just redeem their mim for the underlying, sell it and buy the collateral on another network and mint it on the other network. The collateral might trade lower on one network based on market factors (like if the narrative shifted to that the chain became too centralized or w/e, and this assumes that even the price movement of the underlying overwhelms the over collateralization ratio, it might not) but it would just mean that there would be more or less mim on that particular network as assets are liquidated and not that the MIM itself would be worth less.
In practice the value of the forked collateral is likely to be low, leaving the stablecoins insolvent.