That is where an FRM Charterholder makes a difference
The obligation of delivery lies with the one that suffered the credit loss.In this case the protection buyer on the reference assets.
CDS is an unregulated insurance contract ( OTC derivative). The protection buyer must make the reference asset available on which the loss is suffered in order to make whole. Now whence a credit event takes place the long to the insurance contract ( and long to the reference asset ) may face short squeeze ( CDS is a derivative contract as well that does not require the protection buyer to own the underlying, reference asset which further means that on a given asset there can be multiple CDS holders without owing the asset or having insurance interest ) . Hence the naked contract holder ( in this case the CDS owners) would run for the cover to acquire a piece of the defaulted security that may create a sudden spike in demand that will eventually lead to short squeeze.
To avoid the above, the contract must specify alternate delivery that provides that necessary flexibility to the CDS holders to produce any asset, security as long as the worth is same. But natural, the long would endeavour to acquire the cheapest from such alternate available ones. This would mitigate not only the problem of short squeeze but also would maintain the market liquidity and the sanctity of the overall market.
Hope the above is abundantly clear