Gfycat is a hosting service for (animated) GIF files, which will close on September 1st, 2023. Since some MSE users might have included GIF files hosted on Gfycat in their posts, does the service's closure affect us? How did the Imgur closure get solved?
One possible solution would be to ensure that the posts which include such third-party content get archived on the Wayback machine (https://web.archive.org)
By searching for these URLs on the wayback machine you can capture the page and third-party hosted content.
This will ensure the content is saved in a separate location and can be retrieved later without much effort. This won't be the fastest or most convenient option, but it's very likely to stick around for a long time.
Here's one example.