Characters generally show up in Anchor in the same shape they were when they arrived. There are a couple of medically-equipped containment rooms for sick or injured characters, though, with attending medbots, so the level to which your character is still injured or sick has some grey area. Essentially, it's mostly up to you what level of remaining injury you'd like to play with.
The only exception is for characters with communicable illnesses. More information on that specific situation can be found here.
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Characters generally show up in Anchor in the same shape they were when they arrived. There are a couple of medically-equipped containment rooms for sick or injured characters, though, with attending medbots, so the level to which your character is still injured or sick has some grey area. Essentially, it's mostly up to you what level of remaining injury you'd like to play with.
The only exception is for characters with communicable illnesses. More information on that specific situation can be found here.
Hope this helps!