There are many quests and side quests to complete in Stray, and many of these are required to progress in the story. One of these is getting Elliot to fix the broken tracker, but the robot cannot do so due to its trembling. To stop this, you need to find a blanket, which may leave you wondering where to find the blanket for Elliot in Stray.
This is actually somewhat misleading, as there is no blanket item in the game. Instead, there is a poncho that you can find and give to Elliot to keep the robot warm. This means you need to find a poncho and not a blanket. Here is how to get the blanket for Elliot.
How to get the Poncho for Elliot in Stray
You will need to run around and fulfill other quests to get the poncho. The poncho can be obtained by speaking to Grandma in her shop and fulfilling her request for Electrical Cable. You must find the Super Spirit Detergent to trade with the Barterman to get the cable. Once you do, return to Grandma's shop and hand it over for the poncho.
What to do with the Poncho
When you receive the poncho, you will note that it is too large for the cat and cannot be used in this manner. Hold onto this item and continue exploring the Slums until you receive the broken tracker. You will need to take both of these items to Elliot. Elliot's programming shop has a green glow around it and is just past the main bar (with he red neon sign). You must scratch on his door to get in. First, hand over the broken tracker and then give Elliot the poncho when he mentions shivering. This will warm the robot, and he will fix the tracker.
To get all of the collectibles in the Slums check out these guides to give you a helping hand, All Memory Locations in Stray and All Music Sheet Locations in the Slums in Stray.