There can be vulnerabilities, this is clearly the hottest attack surface of password managers. I remember a few years ago Tavis Ormandy from Google Project Zero found such vulnerabilities in a bunch of the most popular password managers which allowed to steal credentials from a rogue website.

I'd still recommend using a password manager, as overall and in practice the risk of phishing and (re)using (weak) passwords is far greater than this kind of rare vulnerabilities (and also I work for a company that makes a password manager ^^)

See https://lock.cmpxchg8b.com/passmgrs.html if you'd like to know more