Vijñāneśvara’s Mitākṣarā commentary on Yājñvalkya 3 (on expiations), v. 35, explains that even in case of distress a non-Brāhmaṇa cannot take up the profession of a Brāhmaṇa and a Brāhmaṇa cannot take up that of a Śūdra. The commentary on v. 35 also explains that one will need to undergo an expiation ritual (prāyaścitta) because of having undertaken the occupation of another varṇa, once the difficult times are over (see Kumārila’s similar point in text a about expiable permissions). This suggests that

P(taking up the occupation of a kṣatriya or vaiśya varṇa)/being a Brāhmaṇa in distress (and so on for the further varṇas)

is to be understood as an exception to a previous prohibition:

F(perform the occupation of a kṣatriya, vaiśya and śūdra/Brāhmaṇa)

and not of a negative obligation.
It also seems to mean, as Timothy Lubin suggested (Nov 25), that there is no *F(self-harm)/T, since it may happen that taking up the occupation of a Brāhmaṇa would be the only way to avoid dying by starvation, but this still does not lead to a duty to undertake such an occupation.

Moreover, the picture gets more complicated.
In fact, vv. 37–39 explain that

P(taking up the profession of a vaiśya)/(being a Brāhmaṇa in distress)

has some counter-exceptions, namely prohibitions applying to it, e.g.

F(selling weapons)/being a Brāhmaṇa in distress who has taken up the occupation of a vaiśya

Thus, it is possible to have prohibitions within permissions (that are in turn exceptions of other prohibitions)

♦P(x/y) /\ F(z/x)

Then, there is a counter-counter exception, namely:

F(selling/Brāhmaṇa) /\ P(selling/Brāhmaṇa in distress) /\ F(selling sesame/Brāhmaṇa in distress) /\ P (selling sesame in exchange for grain/Brāhmaṇa who can’t perform rites for want of grain).

The commentary quotes Manu 10.91 explaining that if one were to sell sesame in exchange for something else, one would be harshly sanctioned (one will be born again as dog).
v. 41 and commentary explain that the previous permissions are clearly “better not” and that they come with some cost, whereas accepting gifts in case of distress is alright.
So (like in Kumārila, text a above), there are two levels of permissions:

F(selling/Brāhmaṇa)

P1(selling/Brāhmaṇa in distress) —>O(expiation/end of distress) \/ bad karman

P2(accepting gifts/Brāhmaṇa in distress)—>no bad karman

v. 43 (on stealing) follows at that point.
It reads as follows:

bubhukṣitas tryayaṃ sthitvā dhānyam abrāhmaṇād dharet |

pratigṛhya tad ākhyeyam abhiyuktena dharmataḥ ||

“If one has been hungry for three days, he might take some grains from someone who is not a Brāhmaṇa |

If he takes it and is accused, he must say it, according to duty (dharma) ||”

NB: F(stealing)/T is overrun by P(stealing)/not having eaten for three days, provided one is stealing only from a non-Brāhmaṇa (thus presupposing F(stealing from a Brāhmaṇa)/T). The Mitākṣarā commentary
further explains that one can only take enough for one meal and cannot take additional supplies, thus presupposing P(stealing a minimal amount to avoid starvation)/not having eaten for three days.
Now, if one goes on like that for a long time, one might eventually die of starvation (because one is stealing only enough for one meal and only once every three days). v. 44 suggests the solution (the king should take care of one), but this is not a solution one can count on in every case. Hence, v. 43 does not a rule out a situation in which, in order to avoid violating the prohibitions at stake (F(stealing)/T, weakened by P(stealing from a non-Brāhmaṇa/not having eaten for 3 days) and F(stealing from a Brāhmaṇa)/T)) one ends up actually dying.
This further strengthens the point that there is no O(avoid starvation) as the result of F(harm)/T.

The commentary introducing v. 43 states that P(stealing from a non-Brāhmaṇa/distress) only applies to people who have tried all of the above. I am not sure about how to formalise the temporality factor, perhaps something like:

F(selling/Brāhmaṇa)

P1(selling/Brāhmaṇa in distress) /\ distress—>
P1(stealing/Brāhmaṇa in distress)

NB: Kumārila had distinguished between P1 and P2, but by saying that P1 are “general permissions” and P2 specific ones, that is ones explicitly mentioned in text, whereas here P1 can be specifically mentioned and still involve some bad karman.

Appendix: Kumārila, TV ad 1.3.4, text a

[In one case, that of hardship] one does something even without permission, because there is no other way |

[in the other case, that of supererogatory permissions,] one does something else on the strength of a permission: the difference is major ||

And there is a difference between the specific [permission] and the permission (abhyanujñāna) in general (to adopt looser rules in times of hardship) |

[In fact,] the specific [permitted action] is completely free of flaws, the other action has a little (stoka) flaw ||

ekaṃ vināpy anujñānāt kriyate gatyasambhavāt | kriyate ‘nujñayā tv anyad viśeṣaś ca tayor mahāh ||

sāmānyenābhyanujñānād viśeṣaś ca viśiṣyate | viśeṣo ‘tyantanirdoṣaḥ stokadoṣetarakriyā ||

Is the Mitākṣarā just not following Kumārila when it says that even a specific permission can imply bad karman and the need of an expiation? Is Kumārila trying to systematize a complicated series of cases? Or am I missing something altogether?