The house side of stability is the succedent group: the second, fifth, eighth and eleventh, the houses that follow each angle in the order of rising. Greek astrology calls them the epanaphorai, the risings after.
The character the tradition gives them is consolidation. Where an angular house is where a thing happens, a succedent house is where what happened is kept. The second holds the money, the fifth holds the issue, the eighth holds what was inherited or merged, the eleventh holds the friends and the hopes. The group is to the houses what the fixed signs are to the zodiac, and the correspondence is close enough that both were given the same descriptive vocabulary.
The parallel is a real structural feature rather than a modern tidying. Four angles, four succedent places and four cadent places map onto four cardinal, four fixed and four mutable signs, and in a chart where the ascendant falls at the beginning of a sign, the first house is a cardinal sign, the second a fixed one and the third a mutable one, all the way round. Whole sign houses, the Hellenistic method now widely revived, make that alignment exact by construction.
Which is why the two vocabularies confuse people. The houses have modalities and the signs have qualities, the two schemes describe one threefold rhythm, and most astrological writing calls both of them modalities. The atlas keeps the names apart: the house triad is recorded under modality and the sign triad under quality, so a reader can tell which is meant.