“Take no action” borrow
In a normal stock borrow Lenders can elect against Borrower on Loaned Securities — see for example, Paragraph 6.7 of the 2010 GMSLA.
As an example, Borrower borrows Shares in Teldar Paper from Lender. Teldar Paper announces a tender for 20% of the company. The final allocation of the tender is announced at 30%. Lender closes out 30% of Borrower’s position at the tender price. This is called being “held liable”.
An alternative is the “take no action” borrow, where the Lender promises to the Borrower that they will not be “held liable” — i.e., the Lender won’t exercise its rights receive equivalent cash and assets from participating in the corporate event.
Lenders offer TNA borrows at a much higher fee than standard borrows — fair enough, as they are giving up the right to participate in the corporate action, which might be priced attractively. On the other hand the Borrower can participate in the benefits the corporate action without taking any of the risk associated with it — they can eventually give the shares back after all.