Obviously, the economic answer is buy more storage assuming that's a possible answer. It might not be, though--embedded system with no way to attach more storage, or even no access to the equipment itself--say, space probe in flight.
The previously presented answer based on the sparse file system is good (other than the destructive nature of it if something goes wrong!) if you have a sparse file system. What if you don't, though?
Starting from the end of file 2 copy blocks to the start of the target file reversing them as you go. After each block you truncate the source file to the uncopied length. Repeat for file #1.
At this point the target file contains all the data backwards, the source files are gone.
Read a block from the tart and from the end of the target file, reverse them and write them to the spot the other came from. Work your way inwards flipping blocks.
When you are done the target file is the concatenation of the source files. No sparse file system needed, no messing with the file system needed. This can be carried out at zero bytes free as the data can be held in memory.
