I suggest a visit to Pondini's Time Machine FAQ for information about Time Machine. Time Machine does perform a type of archival backup where older files may be removed and replace by newer ones. Time Machine does backup to a HDD contained in the Time Capsule.
TM only deletes older files if they have been deleted from the source and when TM needs space on the backup drive for a new incremental backup. Time Machine "thins" it's backups; hourly backups over 24 hours old, except the first of the day; those "daily" backups over 30 days old, except the first of the week. The weeklies are kept as long as there's room.
So, how long a backup file remains depends on how long it was on your Mac before being deleted, assuming you do at least one backup per day. If it was there for at least 24 hours, it will be kept for at least a month. If it was there for at least a week, it will be kept as long as there's room.
Note, that on a Time Capsule the sparsebundle grows in size as needed, but doesn't shrink. Thus, from the user's view of the TC it appears that no space has been freed, although there may be space in the sparsebundle.
Once TM has found it cannot free up enough space for a new backup it reports the disk is full. You can either erase the backup drive and start your backups anew or replace the drive with a larger drive.
