Hi Larry and welcome to the forum,
Inventory control is one of the biggest issues with dropshipping, you can burn customers very easily with bad control and they can burn you back. Unfortunately, you have very limited options. The quality of the control rests with your suppliers themselves and if you have suppliers that run slack inventory control, then that all flows down hill to you and on to your customers.
The nature of dropshipping makes it absolutely impossible to maintain fool proof stock control for any supplier in reality. Think about it, they could have 500 or more people all selling the same product at the same time all over the world. So even if they have 250 of an item in stock, if they get over 249 orders over night from their customers, then that product goes from being plenty available to zero in a heartbeat.
About the only think you as an agent can do is deal with suppliers that have live stock control so you can see the numbers and monitor sales of the items you are selling. Over a period of a week you can see how many sales of a product are being sold, so you can judge within x amount how long on average it will take for them to run out of stock or at least run low on stock, at which point you can then make a decision as to if you pull your listing on the item in question until the stock numbers get back into what you consider the safe trading zone.
Outside of doing that, you're flying blind and there is always a decent chance of getting burnt I'm afraid.