I have been using a new RAW editor and although it says that the output profile is sRGB, upon opening it, the image has no profile, and right clicking on the image also confirms this. Can you assign a profile to an image that doesn't have a profile?

Also as a side I have noticed that when checking the EXIF data on a TIFF image there are no details of the output profile data, but JPG images do have this information, why is that?