I was wondering if there have been studies on the best practices for the behaviour of a card on selection. I'm in a disagreement with my frontend colleagues that on selection, a card should disappear and move to a new section which only holds selected cards so that the user specifically sees what they have selected. I'm of the opinion that they should stay in place- because a sudden disappearance could be confusing to the user. Also, on search, the cards should disappear if they don't match the search query (even if they're selected). This is a pattern that exists on InVision screen selection too. Are there any examples/studies on this?
I don't think there are any concrete studies on card behaviour specifically, but what IS well researched is the importance of consistent behaviour and (micro)animation. The internet is a wild west of interaction, so users adapt to what they see. Being consistent means they learn how your version works, and animations help users understand changes.
When it comes to Cards, I think Google has things sorted out the best. Cards within the material definition are simply small bits of content that expand to show more information. It makes extensive use of animation to prevent users from getting 'lost' in context; you can see how the card transforms into a full page. This focus view makes it easier to read the content as there are less distractions. Closing the Card means you're taken a level back to where you started. I'm not sure if your co-worker suggested this behaviour or if you did, but it is considered the most default behaviour.
The way search behaves depends on what people do with it. There are plenty scenarios where people ONLY want to see what falls within the criteria, but there are also times where users make a selection of multiple items, using search as a quick way to find them. These items can be unrelated. Invision has the latter use case in mind. It 'remembers' the selected items, even if they are currently not within the search parameters. Again, I don't think this has published researched behind it, but it's a best practice for some.