Is it theoretically possible to dynamically grow array size in stack memory?

Question

I was wondering, given the usual stack memory functioning, whether it is possible for an array like primitive type allowed to grow in size to exist.
The functioning of such primitive type is as follows.

• Any one function is allowed to have only one such primitive variable.
• Appending to such primitive variable is allowed only within the function that it was initialized in.
• If the function that such primitive variable was initialize in is not the last in the stack, such primitive variable is not allowed to grow in size.

I was wondering whether:

• Such primitive type is theoretically possible.
• Whether it is something that is already in use.