is applecare theft and loss valid for phone purchased secondhand without a receipt?

NO. And quite frankly your question sounds incredibly suspicious. A brand new iPhone Pro Max and you bought it second hand? From who or from where? No receipt? How do you even know that the device has AppleCare+ with theft and loss protection, or that it isn't stolen to begin with? That level of coverage isn’t cheap. Please explain more in detail what’s going on.