What happens to a Lightning channel if both nodes break at the same time during high mempool fees?

If I open a Lightning channel with someone and then both of our full nodes happen to get destroyed, while mempool fees are extremely high, then what will happen to our funds?

I understand that the channel (which is actually a multisig address) should close automatically after some time and the funds should return to our separate addresses in fair distribution, but what if mempool is so cluttered that this closing transaction gets purged? Will it ever be rebroadcasted so we can recover our funds even if we never talk to each other and our hardware is destroyed (while we still have our backup phrase)?

submitted by /u/Boriz0
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