TBH 'self custody outside of the main chain' is a complicated subject in itself. And to attach it with a 'security tradeoff' makes it more comprehensive. However, I'll try to be as simple as possible, my limited knowledge and resources on the topic may require your participation in the comments below.
What is Bitcoin Off-Chain Self Custody?
Self custody isn't anything new in crypto circles. In fact, the first ever self custodian Bitcoin wallet released with the origin of Bitcoin itself. In the beginning, these wallets weren't as capable as we have them now. The technical advancements of self custody Bitcoin wallets have even come to a junction which will take them from on-chain to off-chain self custody. However it's not all bright, self custody outside of the Bitcoin main chain may pose a serious risk of a security tradeoff, much similar to non-custodial wallets.
To better understand just go back to 2022, and you realise how important is to hold on to your keys. They don't say incorrectly 'not your keys, not your coins'.

The plant of 'Self Custody Outside the Main Chain' has its roots in the inception of Lightning Network for Bitcoin. Since most transactions on lightning Network are off the main chain, only contracting the main chain when channels open or close for a bundle of transactions.
Major Platforms For Bitcoin's Off-Chain Self Custody
There are many entrants who are ready to roll out purely off-chain self custody vision for Bitcoin wallets.These concepts are in their initial stage and hard to understand but here is my current list:
- Ark
- RGB - Prime
- Utreexo
- Mercury
- Citrea
- Pathcoin
- State channels, Rollups, Drive-chains, other side chains (ie Rootstock or LayerTwo labs)
Need For Bitcoin's Self Custody Outside the Main Chain
The most important of all the problems that Bitcoin faces now is the problem of 'scalability'. The lightning network has solved it a bit but it has its limits. Supposing the world hyperbitcoinizes some day, the on chain fees will rise to the sky. Even the fees for opening a lightning channel would surpass hundreds of dollars! wouldn't that be drastic for the people who will merely hold a few SATS unlike today. We need a solution for them and for the best of Bitcoin as well.

The off chain self custody will off load the Bitcoin main chain in future and Bitcoin will remain open for everyone. If not implemented today, Bitcoin may close doors for small investors or HODLers.
Will the Off-Chain Self Custody of Bitcoin Impair Its Security?
Yes, this is something that we need to address as the primary factor while off-loading Bitcoin's main chain with these innovations. L-BTC (or, Liquid BTC) has emerged out one such player who plans to solve Bitcoin's problems. However there are many concerns that Bitcoiners have already raised considering the overall security of L-BTC.
The lightning network isn't self custodial for everyone as of now. It may be that we see an easier way where Bitcoiners can access to lightning with pure self custody.
Fedimint is centralized because they require trust in external parties a.k.a. federation members to keep users’ coins safe.
So, the idea of enhancing Bitcoin's scalability has come up with some sort of security tradeoff till now. This, however, is yet to be seen if the off chain self custody for Bitcoin can pass the security certificate. So far, I have researched on a few of them and found them really promising. Citrea is one of them and I have recently reviewed it Publish0x. Here's the link:
Exploring Bitcoin's First Ever ZK Rollup
Conclusion
If it wasn't for security, Bitcoin would not be loved that much. I highly suspect if a security tradeoff on the name of solving Bitcoin's problems would become relevant. People entrust Bitcoin for many reasons but security remains on the top of all. So, the upcoming innovations that promise to solve scalablity for Bitcoin by off-loading main chain would require it to do without compromising its security measures. We have already had enough of projects that claim to scale Bitcoin but they are yet to recieve wider acceptance. I also wonder, lest Bitcoin's self custody outside of the main chain does not meet the same fate. The only way to be relevant in Bitcoin space is 'not to tradeoff security in favour of anything'.
If you want to follow the topic and earn sats by participating in discussions, you can join me on Stackernews.com, a platform much similar to Publish0x.
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