The clearest answer is FileMaker's recent knowledge base article on the question of compatibility between FileMaker 11 or earlier products and the latest OS X version 10.9 "Mavericks", which was released in October. http://help.filemaker.com/app/answers/detail/a_id/12643
This article states (in a badly worded manner) that versions 11 and earlier have not been tested or certified for use with the latest version of OS X, and also says that versions 11 and 10 are "not compatible" (how that is known without them having been tested is unclear).
This implies there will be no patches to FileMaker Pro 11 or FileMaker Server 11 if there are any compatibility issues, and earlier versions are certainly not going to be updated. The same would apply if any other new OS or Java version had compatibility issues.
From a historic perspective, it is very rare for FileMaker Inc. to release a patch for an older version after a newer version was released. I found one such update for FileMaker Pro: 7.03va two months after 8.0v1; two such updates for FileMaker Server: 11.0v5 ten months after 12.0v1, and 7.0v4 four months after 8.0v1.
You can see the timeline of patches to earlier FileMaker Pro versions at http://help.filemaker.com/app/answers/detail/a_id/5584/
The corresponding list for FileMaker Server versions is at http://help.filemaker.com/app/answers/detail/a_id/5677
FileMaker 12 has been out for about 19 months, and it seems extremely unlikely that FM Inc would change their policy and patch version 11 this long after version 12 was released.