@Cheryl
"Saving for retirement" is hard to do in Bulgaria because it's the EU's poorest country with some of its lowest salaries. I would find it extremely challenging simply to live on a typical local salary, let alone have any left over to save.
While I love my life in Bulgaria, I can't see it as a recommendable option for younger folks, regardless of whether they're expats or nationals. It might be seen as a harsh judgement, but early career professionals should simply choose to go elsewhere, and find other countries where they can work, earn, and save.
Depopulation (both overall, and relative to the key urban areas) has been a significant issue in Bulgaria for many years. It's clear this has been, and continues to be, driven by its youngsters. They're moving abroad (with an EU passport it's a fairly trivial exercise to work in Germany instead of Bulgaria), or, at the very least, moving to Bulgaria's biggest cities (Sofia, Plovdiv, Varna, Burgas). The following article gives more detail:
To use the UK as a comparison, it has a population of 70 million, and less than 6 million Brits live abroad (8%). Bulgaria's population is 6.5 million, but perhaps 2 million live abroad (30% ish).
I love my life in Bulgaria, and we have a lifestyle that's far beyond what we could afford elsewhere. Moreover, Bulgaria has many great qualities aside from being cheap. But the truth is that I'm old and no longer "economically active" (i.e. contributing to the economy by working), and I already earned my money in very prosperous countries (UK, USA, Finland).
Old Fogeys, such as me, are pretty much irrelevant. Most will stay in their own country (regardless of any perceived decline), and the majority who retire abroad will have a different cost-benefit analysis and choose more traditional retirement destinations (France, Spain, Portugal, Cyprus) even if more expensive. For example, Britain has 12 million pensioners, and only 1 million (8% ish) live abroad! Maybe 250k (less than 25%) in the EU. Specifically, 100k pensioners now live in Spain, and a mere 1,000 or so in Bulgaria, making it a very minority preference.
Bulgaria's own Old Fogeys (who worked many years in Germany and UK) might be more tempted to return (especially if they invested in Bulgarian property while abroad) but, even so, the majority tend to stay in their adopted country.
On the other hand, if you're referring to savings and pensions accumulated elsewhere, I can't even see this as any kind of problem. These days "accessing pension funds" is a no-brainer, as any pension administrator just wants an updated address and bank account and will continue to pay your pension wherever you want. Similarly, with online banking/brokerage accounts you often don't even have to move your savings. My savings certainly remain outside Bulgaria, and its immaterial where I live. My pension isn't even paid to a Bulgarian account.
Arguably, one of the biggest potential benefits of Bulgaria's closer EU integration (Schengen Zone, Euro introduction) might be that it gets MUCH MORE EXPENSIVE. This is bad for me, of course, but could be good for the country. If the cost/salary gap between Bulgaria and its prosperous EU neighbours narrows, it may be able to reverse years of depopulation if its youngsters start finding that it's actually of marginal benefit to move abroad and work in Germany instead. And Bulgaria recognizes the problem, and is already encouraging its youngsters to stay, and its expats to return.