It sounds like you're dealing with a type of expansion joint or caulking material that is used to prevent cracking and allow for movement between the stucco and the driveway. Over time, these materials can degrade or pop out, especially if they weren't installed properly or if there are significant temperature fluctuations.
For a situation like this, you have a few options. First, you can remove the old material and replace it with a new caulking or sealant designed for exterior use. This typically costs between $1 to $3 per linear foot, depending on the specific product and labor costs in your area. If the issue is more extensive or if you suspect underlying problems, it may be wise to consult a professional.
I recommend getting 2-3 quotes from local contractors who specialize in stucco or concrete work. They can assess the situation and provide you with the best solution. You can find qualified professionals on Handyman.com to help you with this repair.
— Assisted answer