Internet is disconnected if VPN application is stopped or closed

What VPN application are you using? Is there a reason why you're not using the built-in VPN in MacOS?

Some VPN configurations will route all IP traffic through it and be at the mercy of all the network restrictions contained in it. So when closing the VPN app, I can see internet traffic being interrupted.

Here's some food for thought: unless you're using a true VPN tunnel, such as between you and your employer's or bank's servers, they are useless from a privacy standpoint.  Read these two articles: Public VPN's are anything but private and Former Malware Distributor Kape Technologies Now Owns ExpressVPN, CyberGhost, Private Internet Access, Zenmate, and a Collection of VPN “Review” Websites. 

That being said one of the most respected contributors to these forums and a respected developer has reported favorably about NordVPN.  So it may be more secure than most of the other public VPNs.