When you plant cucumbers the cucumbers will usually be ready to pick and eat within 50 to 70 days of planting the cucumbers depending on the variety of cucumbers.
The cucumbers will continue to produce cucumbers until it's produced all it's fruit which is around 10 cucumbers per plant.
So once the cucumber plants have produced the 10 or so cucumbers then that's all the cucumber plants will produce and they will no longer grow anymore cucumbers once you pick the cucumbers that are on the cucumber plant.