Nope. You'll either need to upgrade the client, or rebuild it in an 11 environment. Software updating is important as 11 is reaching the end of the support lifecycle, and the file format change is significant for the long term use of FileMaker. I would say you should have the client talk to a FileMaker licensing rep, they may be able to get an AVLA or other agreement for cheaper than they are anticipating. 50 users is a significant system, and they should appreciate the investment that an update represents for their (important) software.
FileMaker Pro Advanced may allow you to copy and paste certain objects and scripts back and forth between 13/11, but you'll be doing a lot of work from scratch.
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And keep in mind that server seats for webDirect connections could end up being less costly than new or upgraded FMP11 seats, while allowing them to use the newer features and stay up-to-date.