Yes, under the Standard 203(k) program eligible improvements include repairing, reconstructing or elevating an existing foundation where the Structure will not be demolished
The Standard 203(k) requires a minimum of $5,000 in eligible improvements.
The Limited 203(k) program may not be used for structural repairs.
For additional information see Handbook 4000.1 II.A.8.a.i.(A)(1); II.A.8.a.vi.(A)(1); II.A.8.a.vii.(A) at https://www.hud.gov/program_offices/administration/hudclips/handbooks/hsgh