I’ve made a PR to add a new policy to disallow using SIGHASH_SINGLE without matched output:

https://github.com/bitcoin/bitcoin/pull/13360

Signature of this form is insecure, as it commits to no output while users might think it commits to one. It is even worse in non-segwit scripts, which is effectively SIGHASH_NOINPUT|SIGHASH_NONE, so any UTXO of the same key could be stolen. (It’s restricted to only one UTXO in segwit, but it’s still like a SIGHASH_NONE.)

This is one of the earliest unintended consensus behavior. Since these signatures are inherently unsafe, I think it does no harm to disable this unintended “feature” with a softfork. But since these signatures are currently allowed, the first step is to make them non-standard.
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