It looks like someone i traded with recently hasn't been on since the 17th of December. What do i do to get the trade closed out?

Have you tried sending him an email?

I didn't know you could email? I though it was only the Deckbox trade chat

Use the Email button on the left of your trade partner's profile page.

If nothing happened after emailing them, how should I proceed? I have a similar situation also.

Trade rule 1.2 Inactivity and unresponsiveness states that you can dispute the trade if the trader's input it required and they have not responded after 7 days.

To dispute the trade: in the trade window click the Support / Dispute button. I would select the Other category since we don't know if your partner received your end or not. Then explain the situation in the details section and Submit.

Thanks.

I'll wait a day and then will use that.