Use a Cloth to Handle Semi-Unsocialized Rats In an Emergency
The only video offered at this time demonstrates using a cloth to move rats who are shy but can be picked up by a human using ungloved hands. The rats are not not happy about it but they tolerate it. One of the people in the video is skilled, the other is learning how to use the cloth.
Do not use the method in this video to work with rats who are seriously unsocialized or frightened, who might be a flight risk, or who are aggressive or may bite. Different management techniques are needed for such a rat.
Using a cloth to move a rat is not a trust training technique. In fact if you ONLY move a rat using a cloth, this does not build trust. In fact it might induce more fear in the rat over time.
Using a cloth to move a rat should be done for emergency purposes or for a brief period only, while trust training is taking place.