From the Phoenix faq:
"Phoenix is trust-minimized, but not trustless. Wise people know that there is no such thing as trustless and that it's all a matter of trade-offs.
The following operations require trust:
channel opening (until the funding tx is confirmed) swaps (you pay upfront, and then our node does the swap) You can configure Phoenix to use your own Electrum server to watch the Blockchain and monitor your channels. This significantly reduces your dependency on third parties to secure your wallet.
For a more detailed overview of the trade-offs, see our blog post."
Thanks. As for my exact question, I've found the answer: If ACINQ disappears, you have to go to your Phoenix wallet (don't uninstall it until you've recovered your funds!) and use the "force close channels" feature. After 5 days your channels will be closed and the funds will appear in your on-chain wallet, which you can restore using your 12 word seed phrase.
All that assuming the mobile app does what it says it does (and it's open source, so has many people's eyes on it). The app stores static channel backups, which allow you to close the channels.
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