Renting / leasing a domain is a pretty good business at times. For example, let's say you have a domain for sale at $5000, and someone wants it but can't afford it. They can lease it from you (paperwork is a must) for an agreed upon sum and duration, let's say $200 per month for a year. You set the DNS or mask forwarding to their site (of another name or upload it to your site as subdomain or otherwise), and you're both happy. You can even do a lease, with intention to buy.
Sometimes a name can be rented for a month or a week for an upcoming event...say a race or a concert. Works well...it's just that most don't think in terms of renting or leasing.