One of the ways a 'stock can be held in inventory' by some entity classified as a MM is if it is a stock is held in a margined account by an individual shareholder at a broker acting as a street name for that individual holder.
That is - if an individual stockholder at E-trade (as one example) has a margin account they generally have agreed to let the brokerage 'loan' out shares in their account to those who wish to short that stock. It's in the fine print of the margin account application.
One of the reasons I have a cash only account - so they can't borrow my shares for others to short.
Alternately - it can be an entity with actual ownership of those shares (or an individual shareholder acting through a brokerage) who allows those shares to be 'borrowed' for shorting for a fee.
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