Old bread becomes sticky
This almost sounds like rope spoilage. From what I've read on various bread blogs, rope spores will cause a typical loaf of bread to deteriorate very quickly in exactly the manner you describe: the center becomes doughy and stretchy. My understanding is that the rope spores can contaminate kitchens and become a real problem for baked goods.

I had a hard time coming up with details on it, but you might want to check the following link for a picture and description:

http://www.intechopen.com/books/advances-in-applied-biotechnology/fermentation-processes-using-lactic-acid-bacteria-producing-bacteriocins-for-preservation-and-improv

I first read about rope spoilage years ago on a bread forum called The Fresh Loaf.

You may also want to check with your local agricultural extension service. There might be testing available.