Where does BERS Pro 4.4 save the files that describe the house?

When you "save" a file it is saved in the BERSProPlus44/HOUSE directory. You can save to any other location using the "save as" function.  You can't just change the file name.

When you "open" a file it defaults to the BERSProPlus44/HOUSE directory but you can change the directory and open a house file that has been put into any directory. The plans are always saved in the BERSProPlus44/PLANS directory.