I'm not sure what is meant by heart doesn't stop growing?. There are heart conditions that enlarge the heart walls and/or heart chambers and referred to as primary cardiomyopathies (enlargement of heart) and have as a dominant feature the involvement of heart muscle itself and that causes growth of the heart walls and there are conditions that dilate (enlarge) the chamber size.
The heart will reach an enlargement that will cause heart failure or cardiac arrest with either increased heart wall growth and/or chamber enlargement.
Does that answer your question? If you have a followup question or comment you are welcome to respond. Thanks for the question, take care.
Ken