Allies Cards in Sickbay/Brig
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  At the end of a player’s Movement step, if his character is in the same location as an ally token, he must encounter that token’s corresponding Ally Card before proceeding to his Action phase.


In the brig, you cannot leave during your movement step voluntarily. Leaving will normally occur as a result of using the action on the brig space. You still have a Movement step, so you're going to encounter the ally before you take an action from a card or on the brig space.


  Players may move out of “Sickbay” without difficulty, but
  not the “Brig.” They may only move out of the “Brig” by
  passing the skill check listed on the location.


In Sickbay, you wait until your turn and would have to decide to remain there during your Movement step. It says "may move out", so you're clearly allowed to stay. This means, however, that you may be starting your next turn there as well.