If it was listed on a stock exchange most exchanges would require a [Market Maker](https://www.investopedia.com/terms/m/marketmaker.asp) (someone who always has an offer to buy and sell).
This is to avoid situations like your scenario.
However if for some reason your scenario did occur that level of inactivity would result in [No Quote](https://www.investopedia.com/terms/n/noquote.asp).
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