We have ordered a half year supply of business card for a certain employee and he just filed a resignation the week after. (he is the one who requested for the business cards). The expense is not high, but i just want to know given these kind of scenarios, can we charge the employee for these expenses since they are about to resign?

my point of view

One thing you don't want is him to go to his co workers and explain how the company is trying to nickle dime him ( and being generally vindictive) how you approach this situation whether positively or negatively you can bet that the other employees will see ( who knows you approach this the right way and you might build moral throughout all your work force).

if this were my company and the guy did that i might be really ticked off ( on the inside) but on the outside i would be the most supportive employer he will ever work for ( you can bet he would never work for me again the dirt bag traitor) good luck with finding a better replacement then the guy leaving.

I've never heard of any company doing that

No, the company pays for business cards and many quit even while having many leftover.

No you cannot, these were needed for your business not his own personal use.

Don't be petty.

Change the name to the new hire.