Let's say I modified an open source app "XYZ", and decided to release it to the public as an closed source app. Is there any FOSS license that would allow such thing?
Most of the BSD-like licenses allow such behavior.
You can read http://en.wikipedia.org/wiki/BSD_licenses for a detailed description of both the license terms, and its philosophy.
Simply saying "open source" can mean many things, all the way from being able to read the source but not being able to do anything with it, up to being able to do anything you want with the source, and everything in between.
In very general terms, what are probably the two most popular styles of licence are "GPL" and "BSD", with GPL characterised as not allowing you to develop a closed source app, and BSD as very much allowing you too (possibly with attribution.)
In specific terms it depends on the exact terms under which you received the source code, and the lack of any such terms defaulting to meaning not allowed by law.
Lots of open source licenses allow this, particularly the BSD and MIT licenses.
They call these "permissive" licenses.
The GPL doesn't allow this; in fact, it was specifically designed to prevent this kind of behavior.
But, you can't apply the license after the fact. The code must already be licensed under a permissive license, before you re-package it as a closed-source application.