The memory slot nearest the Bottom Case can fail due to cracked solder joints which break over time from pressure from the bottom case. The easiest & cheapest "fix" is to just install an 8GB memory module in the other working memory slot since a Logic Board replacement is very expensive. Just make sure to purchase the memory from Crucial or OWC since Macs are very picky about their memory. Make sure to use the tools on the Crucial or OWC web site to get the exact part number of the memory for your laptop (don't go just by the technical specifications).
If you actually mean the memory slot nearest the keyboard is bad, then you can still use just a single 8GB memory module in the good slot, but beware that the slot nearest the Bottom Case is much more likely to fail. I've only ever encountered two MBPros which had a bad memory slot nearest the keyboard.
Make sure to verify the slot is the problem and not just a bad memory module.