No one lives in Eureka, permanently. Eight people are posted at Eureka and they do a tour of duty. In other words, everyone in Eureka is there to do a job. When their tour of duty ends or if their job is eliminated, the person returns south.
Eureka: At its peak, in the 1970s, there were at least fifteen staff on site; in 2005, it reported a permanent population of zero with at least 8 staff on a continuous rotational basis.
I spent a year at Mould Bay on Prince Patrick Island Nunavut a sister site to Eureka. Like Eureka it is also a High Arctic Weather Station . Mould Bay had a population of 12 when I was there. I was the station electronics tech. The rest of the population was two heavy equipment operators/mechanics, a cook, an Officer in Charge (OIC) and the rest were Meteorological Techs.
Running these sites are expensive, but they do establish Canadian sovereignty in this area and provide some benefit to science. Today, satellites can collect most of the same information that is collected by weather balloons at these remote locations. Ozone sounding being an exception.
The Eureka site is important because of the Skull Point satellite down link which provides a feed to the Canadian military listening post in Alert. (Alert's existence isn't classified, but what they do there is)
I agree with cutting unnecessary costs. Cutting PEARL won't shut down Eureka. Abandoning the site would significantly increase the time to repair the satellite down link at Skull Point in the event of an equipment malfunction. Mind you the same problem exists with all the unmanned repeater stations between Skull Point, Eureka and Alert, which can and do fail occasionally. Most weather stuff in Eureka can be automated or replaced by satellite data except the ozone sounding. But that operation (ozone sounding) could be done at Alert. It makes sense to consolidate these sites as much as possible rather than trying to maintain them all. But if you don't use it, you risk loosing it. Denmark had as good a claim on these northerly islands as Canada did, until we established these expensive outposts. Danish explorers were the second people to travel to these lands after the Inuit/Thule peoples. Shutting down these remote outposts risks our claims to this region and all the resources. (Gas, oil, diamonds, zinc, ....)
BTW, I was also posted in Resolute Bay and I was one of the last people to visit Isachsen, Nunavut during a fuel lift about 5 years after it was abandoned. I was sent to retrieve some spare parts.
I was re-assigned to Churchill Manitoba after satellite links replaced the Low Frequency Teletype. I also ran the HAM radio station VE8MC in Mould Bay for a year.