What happens if the fixed shares add up to more than the estate?

Agreed. Yes. Where the Qur’anic fractions come to more than one whole, the shortfall falls on every fixed-share heir in proportion to the share each was owed; nobody is struck out to make the arithmetic work. Technically the base of the problem is raised to the total of the shares actually due — six becomes seven, eight, nine or ten; twelve becomes thirteen, fifteen or seventeen; twenty-four becomes twenty-seven — so each heir keeps the same number of shares out of a larger total, and every fraction shrinks by the same ratio. That is ‘awl. The Kuwaiti Mawsu’a sets out the reasoning — the fixed-share heirs are equal in the ground of their entitlement, so where the fund is short they abate together like creditors, and no heir’s share may be cancelled because each holds it by an express text — and then closes the paragraph: “and this is the view of the four imams”. The classical anchor is ‘Umar ibn al-Khattab. Faced with the first estate whose fractions would not fit, he told the Companions “by God I do not know which of you God put first and which He put last”; al-‘Abbas asked him what he would do with six dirhams owed three to one creditor and four to another, and ‘Umar ruled that the estate be divided bi’l-hisas, pro rata, “bringing on every holder of a right the same reduction the over-subscription brings”. The Mawsu’a records that not one of them objected. The best-known worked case is the Minbariyya, reported by Ibn Qudama: a man leaves a wife, both parents and two daughters; the base of 24 rises to 27, and ‘Ali, asked about it while on the pulpit, answered “her eighth has become a ninth” and carried on with his sermon. We checked this point; the schools do not differ on it.

Shared evidence: al-Mawsu’a al-Fiqhiyya al-Kuwaytiyya, “Irth” sec. 57 — after stating the argument for ‘awl: “wa hadha huwa ra’yu al-a’immati al-arba‘a”, “and this is the view of the four imams” · al-Mawsu’a, “Irth” sec. 57 — ‘Umar’s ruling in the first over-subscribed estate: “ma ajidu shay’an awsa‘a li min an aqsima al-tarikata ‘alaykum bi’l-hisas, wa udkhila ‘ala kulli dhi haqqin ma dakhala ‘alayhi min ‘awli al-farida”, followed by “wa lam yukhalif fi dhalika ahad” · al-Mawsu’a, entry “‘Awl” — the shortfall is spread “hatta yadkhula al-nuqsanu fi fara’idi jami‘i al-warathati ‘ala nisbatin wahida”, on the reasoning that the fixed-share heirs are equal in the cause of entitlement and so abate together ka’l-ghurama’, like creditors on a short estate; al-‘Abbas advised the device and “fa-taba‘uhu ‘ala dhalika wa lam yunkirhu ahad” · Ibn Qudama, al-Mughni, mas’ala 4846 — the Minbariyya: a wife, both parents and two daughters, base 24 rising to 27, “wa tusamma al-minbariyya, li-anna ‘Aliyyan sa’ila ‘anha ‘ala al-minbar, fa-qala: sara thumunuha tus‘an” · al-Mughni, Bab usul siham al-fara’id allati ta‘ul — the Hanbali text working the doctrine: ‘awl arises “fi mas’alatin tazdahimu fiha al-furudu wa la yattasi‘u al-malu laha”, and is “ziyadatun fi’l-siham, wa nuqsanun fi ansiba’i al-waratha” · Surah an-Nisa 4:12 — the half, the quarter and the eighth of the spouses and the sixth and third of the uterine siblings: the fractions that collide · Surah an-Nisa 4:11 — the two-thirds of the daughters and the sixths of the parents, the other half of the collision.

Not covered by this finding: the mirror-image case, where the fractions fall short of the estate and there is no residuary to take the surplus — there the four schools genuinely do differ (see radd) — and the modern statutory inheritance codes of Muslim-majority states, which this entry does not survey — not yet researched school by school. Treat that as open and ask a scholar of your school.