Yes, inmates in medical units are supposed to receive mail. It is not supposed to stop just because someone has been moved out of general population and into a medical setting. That said, delivery can slow down depending on how the facility is set up. Some medical units are in a separate building or even off the main property entirely, which means mail does not always move on the same daily schedule as the rest of the facility. It gets there, but it may batch up and arrive every few days rather than daily.
Keep writing. Do not let the silence on her end stop letters from going out on yours.
As for why an inmate ends up in the medical unit, the reasons vary widely. It could be something routine like a scheduled procedure, a chronic condition that needs monitoring, or a medication adjustment that requires observation. It could also be something more acute, an injury, an illness that developed inside, a mental health evaluation, or a reaction to something. Facilities are not obligated to share medical details with anyone outside, including family and friends, without the inmate's written authorization. So the jail telling you she is in medical but offering nothing else is standard practice, not necessarily a sign that something serious is wrong.
If you are worried, the best move is to send a letter directly to her in the medical unit and ask her to write back or call as soon as she is able. You can also ask the facility whether there is a medical staff contact or patient advocate who handles outside inquiries, though responses vary. If two more weeks pass with no contact, asking whether she can receive visitors or make calls from her current housing status is a reasonable follow-up question.