Any chance we can make our spy be stuck in bondage we get from being hit by enemies like the Autotaper without getting hit by them?
If you complete the game, then the bondage animations will show up on the character customization screen along with the other ones, which is probably the closest thing to what you're looking for.
Otherwise, there's currently no way to remain bound/become bound on command. That shouldn't be too hard to change though if you wanted to download the source from Github and tweak a few things, though.