I have some blue and green doffs. They are bound to my character (the lock symbol). I wonder if it is possible to use them to get white doffs, or are they "till death do us apart" example?

That all depends on how you got the locked doffs. If they are from Lt. Ferra or the KDF equivalent then no, however if they are ones that are bound due to being assigned to ship or as the result of support missions etc. then they can be broken down into 3 of the next lower color.

you just need patience and you can get rid of them, 1 by 1.
See this category on wikia Category:Assignments rewarding duty officers for cultural exchange program assignments.(still need more content)
These assignments accepts bound doffs but when you plan assignments check the full list of doffs not the Recommandations.

this is your chance to get a not bound blue doff from a green bound doff similar to "Asylum"/"Sanctuary" mission when you have a good chance to obtain a blue doff from a green Refugee with at least one trait required
To get lower quality just use a bound doff with a red trait wich lowers the success chances .Even if you fail and lose a bound doff it's not a tragedy lol, the dismissing rewards have been nerfed so it's almost similar to losing the doff

good luck

Yeah, officer exchanges are good here, unless it's a civilian. Bound civilians are nearly impossible to get rid of except by dismissing them.

The only one I can think of is the changeling spy mission.

just found out that if they are bound then they can't be used for officer exchange missions (Feresan, Cardassian etc) or for reassignments.