As I understand it, you are asking for an example of a good or service whose demand would be perfectly elastic. If so, the answer is that any good (I do not think services are likely to fit these criteria) in a market in perfect competition would have perfectly elastic demand.
Perfectly elastic demand occurs when a change in price causes an infinite change in quantity bought. If you raise your price at all, you stop being able to sell any units of your product. If you drop your price at all, the entire market starts to buy from you.
In perfect competition, this would be true. In perfect competition, every seller is selling a homogeneous product. This means that all of their products are exactly the same, both objectively and subjectively. Therefore, no one will be able to differentiate between the products on any grounds other than price.
An example of this could be agricultural produce. If 1000 farmers all produce wheat of the same variety and grade, there is no reason for a commercial buyer to differentiate between them. They are all selling the same product. This means that the buyer will not buy from any farmer who tries to sell for a price higher than the others. Similarly, the buyer would buy as much as possible from any farmer who lowered their prices at all. In this case, demand would be perfectly elastic. Any commodity, then, that is truly homogeneous and whose market is in perfect competition will have perfectly elastic demand.