Where is Yagrum during the events of ESO?
• Dwarves disappear around 1E 700
• ESO is in 2E 582
• Dagoth Ur makes a reappearance around 2E 882.
• Morrowind takes place 3E 427
We know where Divayth is, and we know that there is not a Corprusarium and Dagoth Ur is still "dead": or inside Red Mountain, but no one has contracted his form of Corpus at this time. (Yes, there are the people in Craglorn, but there are other types of blights like there are strains of the flu) So it is safe to say that Yagrum has not contracted the disease yet, is still somewhere in the outer realms, or wandering through Tamriel.

Is Yagrum walking around Tamriel or still trapped in an Outer Realm? Let us take a look back at what Yagrum Bagran's text says from Morrowind to see if we can try to figure out where he may be at this moment.

"Hmm... I cannot say what happened. I was not there to observe. I was in an Outer Realm at the time, and when I came back, my people were gone. I left Red Mountain, wandering Tamriel for years, searching our deserted colonies, looking for a survivor or an explanation. Then, a long, long time ago, I returned to Red Mountain, still looking for answers. Instead, I found corprus disease, and I have been here ever since. I have theories, if you are interested."

He states that he contracts Corpus when he returned to Red Mountain which was "a long, long time ago" Let's say Dagoth had Corpus spreading around in 2E 882 and Yagrum contracts around this time as well This would mean he had Corpus for about 441 years during the events of Morrowind. 441 years could be considered a long, long time.

Yagrum contracts corprus around 2E 882, and between then and ESO in 2E 582 is 300 years.
Yagrum says he wandered around Tamriel "for years". The fact that he thinks 441 years is "a long, long time" I doubt he would think that 300 years would just be considered "for years" 300 years is a long time as well.

Back to "a long, long time" and 441 years. This is what Yagrum considers a decent amount of time.

300 years is a long time to be wandering Tamriel looking for his Dwemer brethren and he doesn't say he was looking for them for a long, long time, he just says he was looking for them for years. So how many years was he looking for them? 300 years does not seem likely.

I think it would be more apt to say that Yagrum was looking for Dwemer for about 100 to 150 years before he contracted Corpus. 100 years is not that long when considering any Mer life span. This would mean he came back from the Outer Realms around 2E 732-782. Well after the events of ESO.

Our last living Dwemer is most likely still wandering somewhere in the Outer Realms during the events in ESO. But which realm is he in? I have no idea. I hope the developers decide to bring in a quest where we travel to a Daedric Realm and stumble upon the last living Dwemer.