Who owns the IP a contractor or departing co-founder created?

The person who created it, unless they assigned it to the company in writing. For contractors, this surprises founders most: the US work-for-hire doctrine applies to copyright, not patents, and even for copyright it only covers contractors in narrow circumstances, so a freelance engineer who designs a novel mechanism owns the invention and the code unless the consulting agreement says otherwise. Paying the invoice buys the deliverable, not the intellectual property in it. The fix is an assignment clause in every consulting agreement before work starts, plus an obligation to sign confirmatory assignments later, since a contractor who has moved on has little incentive to help.

For a departing co-founder, the question is what was assigned to the company at incorporation and what the founder agreement says. If everything created before and during the company's life was assigned in a founder IP assignment and the person is still bound by it, the company keeps the IP and the founder keeps whatever vested equity they earned. If no assignment was signed, the departing co-founder still owns their share of the inventions they conceived. In the United States, joint owners of a patent may each use and license it without the consent of, or accounting to, the others (35 U.S.C. 262), so a departing co-founder could license your core patent to a competitor. In the UK, co-owners cannot license without the others' consent, which leads instead to deadlock. Both outcomes are worse than a signed assignment. If a co-founder is leaving and nothing was signed, negotiate the assignment as part of the separation agreement, while there is still something to trade. See also Do I need an invention assignment agreement?