Do you really need examples of this? There are countless of them, some programs you cannot have missed are PRISM, STATEROOM and BULLRUN but there are more of them too.
I'm not so much asking as a gotcha, as modern examples of this kind of backdoor (or published encryption weaknesses) would be a big deal. I realise that there are many other tactics that states, especially the US, pursue that undermine privacy online. These just seemed weirdly specific to projects that the US has, in fact, failed to pull off for years: compelled insertion of code, and deliberately weakened encryption.
(ObContext: I worked at EFF during the Snowden revelations, and worked on understanding the impact of PRISM, and Bullrun specifically.)
> PRISM is a code name for a program under which the United States National Security Agency (NSA) collects internet communications from various U.S. internet companies - https://en.wikipedia.org/wiki/PRISM
> STATEROOM is the code name of a highly secretive signals intelligence collection program involving the interception of international radio, telecommunications and Internet traffic - https://en.wikipedia.org/wiki/Stateroom_(surveillance_progra...
> Bullrun (stylized BULLRUN) is a clandestine, highly classified program to crack encryption of online communications and data - https://en.wikipedia.org/wiki/Bullrun_(decryption_program)