Gently separate the offset from the rest of the plant and replant it so that the base of the offset is in contact with the ground. I would make sure it is in a location that I see every day. In my case, plants in a "critical" state are planted in a small pot and placed on a table on the back porch where I pass every day. I like to use small pots for these, then water gently (or mist) a few times a week. The small pot allows the plant to dry a bit between watering's, so chance of rot is minimized. Check daily. The plant in the pic looks really healthy, so should make a full recovery.
