I know nothing about the topic but my best guess is that the white dwarf will have a mass comparable to the current Sun's mass but concentrated in a much smalle

I know nothing about the topic but my best guess is that the white dwarf will have a mass comparable to the current Sun's mass but concentrated in a much smaller space, and so some objects may thus be able to orbit much closer and experience strong tidal forces as the gravitational well will be much steeper.