The rules are extremely simple,

1) One has rights if he/she has bought options
2) One does not have any rights if he/she has sold (written) options
3) One has obligations if he/she has sold (written) options and the options are expired in the money

And therefore, if you have sold (written) puts, you do not have any rights (or choices), but if the stock prices drop below the striking price, you have the obligation to purchase the said amount of stocks at the striking price.

There are three ways to close the deal,

1) Sold put bought back
2) Expires worthless
3) You get stock assignment

Also, past is always past when options expire.