You are correct. She would need to file a return reporting the pension and SSDI and indicating she can be claimed as a dependent on someone's return. Likely the SSDI will be non-taxable since you mention a small pension so she should get the withholding refunded.
As for you claiming her as a dependent, below are the rules extracted from Publication 501, Table 5 for you to claim her as a qualifying relative. She will most likely meet tests 1, 2, and 4 but test 3 is challenging and verifiable on her tax return.
Her gross income will likely be her pension, but if any of the SSDI shows as taxable on her return it too counts as gross income.
- The person can't be your qualifying child or the qualifying child of any other taxpayer.
- The person either
- (a) must be related to you in one of the ways listed under Relatives who don't have to live with you, or
- (b) must live with you all year as a member of your household (and your relationship must not violate local law).
- The person's gross income for the year must be less than $4,700.
- You must provide more than half of the person's total support for the year."
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