afraid of snatching vs afraid of being snatched

There is possibly an echo of

• You are possibly worried about burglary.
• You are possibly worried about being burgled.

where the two variants are virtually interchangeable (and acceptable).

However, there are few cases where both variants are interchangeable.

• You are possibly worried about rape / being raped. (both variants idiomatic ... sadly)
• You are possibly worried about being burgled. (far more likely version)
• You are possibly worried about being attacked. (only normally idiomatic variant available)
• You are possibly worried about arson. (only variant available)
• You are possibly worried about fraud. ('being defrauded' less likely)

Here, unless 'snatch' is slang for 'kidnapping',

• You are possibly worried about your bag being snatched.

is probably what is required. The variant '- You are possibly worried about bag-snatching' is less likely, though quite grammatical, and not unidiomatic in a formal register. It doesn't overlap in meaning completely. And 'You are possibly worried about rape', for instance, can have the non-personal sense 'in your capacity of Police Officer in charge of curtailing Violent Crime'.