How did Soap get away to freedom but Price ended up in gulag?

Solution 1:

I is not completely certain that this happened this way since there are some holes filled by fans and rumors but this is the accepted story.

A Russian medic can be seen trying, seemingly in vain, to revive Price, but Soap and Price are taken to a Russian hospital.

Sometime after healing from their wounds sustained from the Zakhaev incident, both Price and MacTavish were reassigned to General Shepherd's newly formed-elite unit, Task Force 141. Acting as the field commander for the regiment Price led his new unit on countless covert operations with the key goal of capturing/killing Vladimir Makarov.

On October 8, 2013, Price led a joint Task Force 141/Delta Force operation codenamed Operation Kingfish, to raid an Ultranationalist base in Ukraine suspected to house Makarov. Price conducted the raid along with Soap, Simon 'Ghost' Riley and Delta Force operative Sandman.

Price was captured by Makarov's men and imprisoned in a Gulag east of Petrovpavlosk, Russia, and was designated "Prisoner 627". Price would remain imprisoned in the Gulag until 2016, where he was rescued by Task Force 141 when they attacked the site to recover him.