No this is not normal. You have a water intrusion issue. It sounds like its coming from the inside of the house if the stucco is dry on the outside. This could be a plumbing leak if the damage is isolated to one area.
Hi , there is few reasons it’s can happened
The most commoned is …
Today when we are doing a exterior paint project the first step is the power wash with 2600 psi machine , then we are diging “6” inch dip all around the house ,
Why we do it ?
Power wash - power was is to remove all bad and damage stucco that not visible, the stucco that weak .
“6” dig deep around the house
We do it because we want to do all prep work from the footing up
The reason is we home owner have some sprinkles system or and dirt around the stucco
The water coming from under the line for the stucco, and coming up and then we see damage around the house on the ground level.
To make sure it’s not happened again
It’s very simple think to do , need to make sure the the prep work under the ground level (footing ) will be protected. Then no water will come up and damage the stucco .