If so, does the dependent lose the right to qualify for a non-conditional green card?
Yes, this can be done. You will need to notify USCIS and request that the dependent be removed from the I-829 process. The act of doing so will mean that the dependent is no longer a conditional resident - if they are in the U.S., they should depart as soon as possible.
Yes, a dependent can withdraw their I-829 petition. And yes, if you do not receive an I-829 approval, you do not receive a permanent green card.
Need more facts to advise. If dependent wishes this, then yes, but not if principal is trying to have dependent withdrawn. After conditional residence is granted, this belongs to the beneficiary and not the principal.
It is very unusual but if the dependent wrote to USCIS withdrawing only his or her application, they may cease to process his or her case. If you are seeking to do this as the principal, that may be possible, but I doubt they have a hard and strict rule for this. Need to be careful they withdraw only the derivative and not the principal, because if in the U.S., you may have to leave asap.
