Any candidate who responds to a notification about a new opportunity will appear in the Applicant tab, whether they have requested to work, expressed that they are not interested, or cancelled their request to work.
However, as an admin you will only be able to assign candidates who have requested to work--as visible by the green plus marks that can be seen next to their names in the Applicant tab.
What if a candidate isn’t able to be assigned, what if they don’t have that green plus mark next to their name? If you head to the Mission view and click on Assign Someone, you will be able to see who is available (hint--it will be the same candidates who had the green plus mark next to their name). If you click on View Others, you will be able to see which other candidates were in the Applicant tab, and why they cannot be assigned--because they had cancelled or declined.