When a membership subscription is made available for monthly payments (see this article), ManageMyMatch can continue to take monthly payments for ever until the member (or the membership secretary) chooses to stop the subscription.
But this feature only happens when the membership does not have a fixed start date (In the Timing section of the Product setup screen under Manage clubs, this would mean the Set start date to beginning of period is ticked).
You can still choose a period (months or years) over which the subscription product applies, though the difference is more subtle than the case where the subscription is bought up front for a fixed period.
For monthly paid subscriptions, the user can choose to stop payments at any time. This gives greater flexibility and freedoms to the member and the club may choose to be compensated for this by charging a higher fee than a fixed term contract.
When setting up the subscription product you can set a different price for both a fixed term and a monthly payment term option. If either one is zero, then the relevant option is not available to the user. For example, if you set a monthly subscription priced at 0 for a fixed term and £100 for monthly, then the user would only be given the choice to pay by monthly instalments.
With a one year monthly subscription, what happens is that ManageMyMatch will set up a payment schedule for the whole year given the current price set for the product. Then, as each month passes, the expiry of the subscription is extended and a new payment date is set for a year forward. This goes on ad infinitum, until the member stops the subscription. The key point is that a year's worth of payments are "locked in" for the member - once a payment is listed on their schedule it will never change. So the monthly payment set a year hence is based on today's price as set up on the subscription. If you change the price of the subscription, the scheduled payments for the next year do not change - only the monthly payments added a year hence will reflect the new price.
If you'd like any changes to your subscriptions to take more immediate effect, then you can set the subscription period to be less than a year. A month for example. In this case the member will only see the next payment locked in at any one time and each payment added just 1 month in advance will reflect the current price set.
When the member (or you as a club official in Manage members) stops the subscription (There's a Stop button next to the subscription in My subscriptions), the subscription is set to expire as far as the current month's payment covers - i.e. within a month. All subsequent payments are stopped. While the subscription is running its course up until that date, the member may change their minds and restart the subscription if they want.
Only the member themselves can choose to pay monthly for themselves or for their family members. As a club official or membership secretary this cannot be chosen on behalf of a member. This is because it involves forward financial commitment which can only be responsibly taken on by the member themselves.