Where do researchers get the money to replicate others' work?
In my field (cognitive science), your supposition that replication is primarily pursued by investigators prior to extension is true. For example, I have an idea while reading a paper on learning targeted movements, I first implement the paradigm as described (either an exact replication or a conceptual replication) and then I extend it to test my idea. Thus, the money for this comes from the same places that the money for all research comes from: largely from government allocations and grants, partly from NGOs and industry.

However, there has a been a recent trend--again, in my field, but as part of a larger movement in the social sciences--to improve replicability of results. This has included fostering availability of code for software projects and pursuing independent replications purely for their own merit. Last semester I attended a talk on a set of these replications, which, along with similar attempts from other labs, were pushing to overturn the original result. In these cases, the money to pursue the replication is probably somewhat independent from other projects of the researcher. This means funding agencies would be unlikely to provide a grant entirely for this work, so it is probably going to be supported as a passenger on previously funded work or on University funds (e.g. start up and salaries).