The phrase that which often could be shortened to one-word equivalent pronouns such as what and whatever. The main exception is when that which refers to an antecedent.
In these examples, that which is just a wordy way of saying what and could be shortened:
That which has been obvious for some time now is finally being officially acknowledged. [CNN]
Maybe that which doesn’t kill us really does make us strong. [Sydney Morning Herald]
But it is a trifle unfair that new uncertainty has been ladled on top of that which already exists. [Daily Mail]
And in these examples, that which is justified because it has an antecedent:
The bill seeks to restrict Web sites from collecting information to only that which is “necessary to process or enforce a transaction or deliver a service.” [Washington Post]
For instance, we have no large-scale sub-prime market similar to that which crashed U.S. housing. [National Post]
This collective amnesia, like that which erased Scotland’s leading role in the Caribbean slave economy, may be deliberate. [Herald Scotland]
The antecedents of that which in these examples are, respectively, information, large-scale sub-prime market, and collective amnesia.