Your shrub's rapid decline after removing a basal shoot suggests one of two scenarios: euonymus scale infestation (if it's a euonymus) or transplant shock (if recently moved). The "white dust" description points strongly to scale.
If it's euonymus with scale, aggressive treatment now can save it. If shock, patience and consistent care are your only tools.
Tall Cactus Basal Rot: Thin Species = Cut and Root, Fat Species = Lost
Euphorbia Cold Damage: Fast Rot Spread, Basal Damage = Likely Loss
Saving 'Jelly Bean' and Hens & Chicks from Georgia Rains
Dying Orchid with No Leaves: Crown Rot Likely Fatal
Unidentified Orchid Decline: Need Species ID for Diagnosis
Rescuing a Rotting Cephalotus: Emergency Repotting Guide
Reviving a Shipping-Damaged Fork-Leaf Sundew: Patience and Proper Care
Indoor Yucca Yellowing: It's Not the Weather, It's Light or Water
Reviving a Drooping Arrowhead Plant (Nepthytis)
Helping a Rain-Damaged Bougainvillea Recover
Mystery Plant from Downsizing Neighbor: Aluminum Plant / Watermelon Plant (Pilea cadierei)
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