The owner of a stock owns a piece of the company. Regardless of the currency, what they own is a piece of the company. When I look at a stock quote it is in US dollars, but that simply is the last price it traded at. Someone in Europe looking at a quote for the stock in Euros is just seeing that last transaction expressed in Euros. If the Euro “failed”, whatever that means, shares are still shares, and the owners of the shares still owns the same piece of the company. Now, seeing a price might be difficult to impossible, but since the ownership is not of currency but of shares the owner hasn’t lost anything when the dust clears.
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