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Expiration

Time limited contracts

When a blockchain is established, the genesis block can establish rules regarding how long title to shares may be held. In this way, shares which are lost to their owners are returned to the community. Consider a hypothetical chain which establishes ownership in a company with 100 shares, divided equally among 10 shareholders. The company charter states that a majority of outstanding shares must vote in favor of amendments to the charter. Over time, some of the shareholders sell out and others consolidate their holdings until at one point a husband and wife end up controlling 60 of the original 100 shares. Each maintains their private keys which control the shares voting rights in their heads and nowhere else. One day they are both killed in a car accident, leaving the remaining 40 share holders unable to amend the company charter. With share expiration, after some time those 60 shares will expire, no longer being counted towards the outstanding shares, leaving the remaining 40 share holders in 100% control of future issues. The share owners may "refresh" their shares at any time by assigning them to themselves as new shares, restarting the expiration clock, for the cost of recording the assignment.
1Hopefully the cost of recording is trivial as compared to the value of the shares.
The time of expiration should be long enough to not be a nuisance requiring constant record updating, but short enough to not paralyze the company in situations such as the above. Note that with an expiration period of a year, that would give the heirs of the deceased time to potentially obtain physical and/or legal access to the keys to the shares and assume control of them. Also note, if the organization which is controlled by shares in a blockchain is of so little interest to the owners that they do not bother to refresh the timer on their ownership shares, that allows control to pass automatically to those who are still interested to keep their share registrations up to date, and also allows an organization with essentially zero interest in it to definitively cease to exist.
2perhaps to be replaced in the future by a new organization, if interest is ever renewed in the cause.

Coupons

In addition to the shares used in recording on the blockchain, contracts on the chain may also be given various forms of expiration dates, such as coupons for discount or free goods which expire if not redeemed by a certain date/time. This concept of time limited value is nothing new in financial contracting, but having it electronically managed as fungible items at such a small scale is something that has not been widely practiced to date.

Expiration as a parameter

How shares expire can be controlled as a parameter of the blockchain.

Per contract expiration

When contracts are recorded (not as shares on the chain, but as their own entities recorded on the chain), there can be various forms of expiration decided on a per-contract basis.
3though, there is value in standardization - if a form of expiration is unfamiliar it can be difficult to asses its impact on value
This expiration can also be used as a security mechanism - when a contract expires quickly, if someone manages to obtain rights under the contract through coersion or stealth they will also have to exploit the value of those rights before they expire, reducing their value to the nefarious party. Expiration can be a strong reassurance of limits of liability: when rights issued under a contract expire, then liability is no longer a consideration. For example: a contract can state that value must be redeemed (transfered) through recording on the primary blockchain record before a specific time. Once that blockchain has passed that specific time, the value in the contract can no longer be redeemed and the contract presents no more liability.
4Fancy expiration schemes might have soft expiration limits where liability reduces over time, eventually reaching zero. The simpler approach is 100% value until the cutoff time, then zero afterwards - this is the scheme proposed for share assignment authorizations: if recorded on the blockchain before a certain time, the authorization takes effect - if the blockchain moves past the agreement expiration time before inclusion of it, then the authorization is null and void.