Second hand or used graphics card is similar to buying a used CPU. Both of them are used for processing and can be overclocked. But your chance of getting a good graphics card in working condition is better than getting a used processor or hard disk. This is because there are plenty of high end gamers out there who are constantly changing their graphics card to the latest. You can see lot of them offering to sell their graphics card in good working condition to partially fund for purchasing the new ones.
Unlike Processors, Graphics Card can be refurbished. Lot of things can go wrong in a graphics card and most of them are repairable. The chips inside a graphics card are only produced by the manufacturer. So in case of repair, it has to be done by the manufacturer which will be of good quality. The other damage that can happen is to repairing heat sink or fans, which should not be a problem as it can be fixed by any tech shop repairs.
Just like processors, another risk of buying a used graphics card is the possibility of overclocking. Some of these graphics card may enter the second hand market because the original owner must have tried his own overclocking methods, but failed to get the desired results. Taking overclocking to dangerous level can also reduce the performance as some of the chips might be damaged. Unfortunately, there is no way to find if the graphics card was overclocked and if damaged, to what extent. You will have to trust the seller.
A refurbished or repaired graphics card is a safer bet, compared to non-refurbished second hand product. Considering the repair is done by original manufactures, you may trust them to give maximum performance.
If it is worth, there is no problem in going for a used graphics card. Modern Intel or AMD processors have its own graphics processing unit inbuilt and also the motherboard also have inbuilt graphics card. So, even if your graphics card failed you still can work on your computer. Before buying the used graphics card, also insist on an agreement with seller on a returns policy within a certain time period.