can non paying bidders still bid on other auctions while a case is open against them?

I have opened 2 unpaid item cases and have had no response after initial invoice or the others sent after.  Opened unpaid cases and still no response.  I am wondering if they are still able to bid on items while a case is open against them.  I am hoping not as why would they even care to complete transactions if they can just go about their shady business as usual. 

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You can block anyone you want from bidding by adding them to your blocked bidder list.