often relying on getting a warrant post hoc or lying to establish probable cause.

https://en.wikipedia.org/wiki/Parallel_construction

Here's a whole ass Wikipedia article on the very subject, because it's been so widespread for so long it has a fucking name.

https://en.wikipedia.org/wiki/Hemisphere_Project

Here's a Wikipedia article on the mass surveillance by the DEA, which is where the data used for parallel construction was sourced.

https://www.reuters.com/article/us-dea-sod-idUSBRE97409R20130805/

Here's a good example from the first Wikipedia article about how the Feds pass signals intelligence to local law enforcement so they can start cases and claim they found the initial evidence some other way than illegal mass surveillance.

For more history about attempts to install backdoors, see:

https://en.wikipedia.org/wiki/Clipper_chip