In order to convert .abk files to .doc documents, you first have to recover the backup and then use the File ► Save as.. function in Ability Write to produce your document. That is, if your document backup (.abk) is valid and not corrupted.
Convert Ability Write document backup to Microsoft Word document (prior version 2007).
We have found one software suitable in our database for this conversion.
Microsoft Windows software - convert abk to doc on Windows
A fully featured word processor from Ability Office software suite
Convert from abk file format
The table with program actions contains information about what each program is capable of doing with their files. This may be a good pointer for further searches for certain file conversions and help you find the converter you are looking for if our search result is insufficient for you. However, it is far from perfect and may sometimes show results which are not really usable because of the nature of the software handles the files. So a conversion that appears as possible, just because of matched actions, may in fact not be possible.