Do shields prevent Sonya from gaining Fury?

Solution 1:

Short: No, they don't. Sonya gains fury when shields are active.

As the description says:

Generate Fury by dealing and taking damage. Using Abilities gives Sonya increased Movement Speed.

I tried to capture it in screenshots, here's the output:

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Both health bar and fury bar go up as Sonya takes damage and heals herself at the same time.