If you as a US citizen move to Euroland it should be pretty easy to get decent local currency exposure on parts of your stash in an US investment account. One is by buying a US-listed equity fund/ETF with European exposure that does not hedge its FX risk, that effectively means you get capital gains/losses and dividends in Euros (+ maybe some GBP and other smaller currencies) albeit yoiu will need to exchange into EUR yourself as you go. If the USD weakens, the USD value of this fund will go up and conversely it will got down if the USD appreciates.
It should also be fairly straightforward to get bond exposure in Euros, a lot of US-based companies issue debt denominated in EUR, but one problem here might be that they require a fairly large minimum purchase per bond making diversification difficult. Buying EUR-denominated government bonds is maybe easier and there is also likely to be an ETF tracking that, but for it to be actual EUR exposure it needs to be something that doesnt hedge its FX risk which bond funds tend to do.
Same principle applies to any place, but the choice of ways to do it is more limited the smaller the economy you are moving to.
If you live in a country but have no income in local currency to cover running costs of living you have substantial FX risk.