If two people who are unmarried share a joint account, can Medicare take money from that account if one of the owners closes the account?

Medicaid does not "take money". Is one of you in need of Medicaid? Co-mingling your money will cause a problem. Medicaid looks at any accounts with the applicants name on them theirs. The other person has to prove differently. There is a a 5 year look back with bank statements. It maybe be questioned why the acct was closed.

Medicare is a health insurance. It does not pay for care.

No one can take money from a closed account.

I think you mean Medicaid, not Medicare. Medicaid is a state-run program so what it does can differ from state to state, therefore crowd-sourcing your answer from a global forum may not produce an accurate answer. Best to contact the Medicaid office for your county (or look online) to ask that question. It can get complicated fast, so maybe consider investing in a consult with a Medicaid Planner (yes, there is such a job description) or elder law attorney/estate planner. You won't regret going into it with thorough and accurate information. It may make all the difference in qualifying or not. You need to also be aware of your state's Medicaid look-back period for the application, which can be as long as 5 years (like in my state).