The UTXOs on chain have not changed, but you can think about it as a system of balances off-chain that have been updated. I tend to think that we should keep only small 'cash' balances in a lightning wallet, like your real world wallet, and sweep any larger amounts into your cold storage (on chain). Muun offer a good service that lets you send on chain as well, so if you are worried you can send LN payments to Muun then transfer on chain into cold.
Discussion
Heard about that. Muun is non custodial right? And if i remember they store tge wallet balance on chain?
That's also my understanding - they use LN via 'submarine swaps' where the LN payments take place whenever you send or receive. Ostensibly non-custodial, although they don't use a traditional 12/24 word list (and I have not yet done a full delete ans recover). I'd suggest using them as a simple workaround to get comfortable with moving from LN back in chain and vice versa.