The other option is for the DLNA to send the subtitles along inside the video image. srt, etc), and this varies from vendor to vendor. But, not all subtitle formats are usually supported (e.g. Usually, the subtitles have to be in the same folder where the video is, and with the exact same title.
The first one is that the TV supports the playing of the subtitles, in which case it will request the subtitles from the DLNA and display it (usually, there's a button on a tv remote to turn on the subtitles explicitly - on Sony there's a button with four dots inside the square (.) that turns on the subtitles).