Four years ago as Viviette Applewhite, now 93, was making her way through her local Acme supermarket, her pocketbook hanging from her shoulder, a thief sliced the bag from its straps. A former hotel housekeeper, Ms. Applewhite, who never had a driver’s license, was suddenly without a Social Security card. Adopted and twice married, she had several name changes over the years, so obtaining new documents was complicated. As a result, with Pennsylvania now requiring a state-approved form of photo identification to vote, Ms. Applewhite, a supporter of President Obama, may be forced to sit out November’s election for the first time in decades. Incensed, and spurred on by liberal groups, Ms. Applewhite and others like her are suing the state in a closely watched case, one of a number of voter-identification suits across the country that could affect the participation of millions of voters in the presidential election.