Becky Albright was a witness to one of Scarecrows crimes; when she refused to recant her testimony he began kidnapping her and exposing her to fear toxin in order to discover her greatest fear. Becky appears to have some deformity such as scoliosis or even cerebral palsy and is terrified of how other people view her, a trait that Jonathan Crane shares.
The Scarecrow stopped tormenting her and attempted to recruit her as his "Mistress of Fear" - Ms. Fear (it appears he had developed a crush)
Becky refuses and is saved by Batman who remarks "looks like she is your greatest fear Dr. Crane"
Becky never took on the mantle as mistress of fear despite many fan wanting to see her become the Scarecrow's love interest.