In general, the financial health of a token economy might be described as the hodl pressure (or buy pressure) outperforming the sell pressure.
Tokenized access leverages a token holder's identity to give them special privileges to opportunities, events, and information. This is a rapidly evolving space with many emergent new use-cases and possibilities.
Examples
Staking has been used in Proof of Stake (PoS) consensus systems for years.
Today there are now both consensus systems like PoS as well as incentives for liquidity providers (liquidity mining) that both provide rewards and increase hodl pressure for a network.
Vesting tokens allows for a network to distribute the tokens without giving the owners opportunity to move them for some amount of time. This method is used in modern ICOs.
Examples
NFT mining is a new use case pioneered by the $MEME economy. This encourages holders of the token to stake them into contracts; over time those who stake will accumulate a new token they can use to purchase NFTs (see: social tokens).