@lillianroot
Getting Deja Vu, I feel like I've seen this question posted a while back.
(my assumption is that they plugged into the layer 3 switch instead)
I doubt it. They most likely did one of two things... they either spanned the appropriate VLAN out to that switch or put the end-users on a different VLAN and forced them to re-address their equipment.
Are the layer 3 switches allows the VLANS to pass traffic across a trunk through routing but the layer 2 switch can't do that feature?
A layer 3 switch is a switch that also has routing functionality. However, it would need to be configured and implemented properly to actually route traffic. The fact that the switch has layer 3 functionality doesn't necessarily mean it's routing traffic. So, the short answer to your question is no. A layer 3 switch will pass the same VLANs over a trunk that a layer 2 switch will. The difference is layer 3 switches can also do static routing, dynamic routing, etc.
Best practice is for every closet to have unique VLANs. So, if the VLAN you're looking for isn't on the switch, it was probably left off by design. So, someone had to make a decision whether to span that VLAN out to that switch or force the end-users to re-address their equipment on a subnet that exists in that closet.