S. R. Faruqi:

In the verse the point is that our wrecked and bad condition is in reality due to our disgrace; for this reason, we receive no honor. But the fame and reputation of beloveds is brought about by this wreckedness and ruination of ours. Reputation, because it's the special accomplishment of beloveds to ruin lovers entirely. However much the beloved would practice/show 'belovedness', that's how much the lover will be ruined. Thus if in a whole populous town the lover's house alone is the one that's ruined, then the reputation of the beloveds has been established through this very lover.

Another point is that he feels no sorrow at his own destruction; if he's become a means for the fame of the beloved, then he certainly feels pride at this. There's also a fine implication in the verse, that on the basis of the wreckedness (destruction) of the heart, the house is desolate-- that is, if the heart was destroyed, then it wasn't possible for the house to remain inhabited.

Ghalib has expressed this theme [in Persian] with his special complexity and splendor:

'She needs us for the spreading of her fame,
The way flame is indebted to grass and straw.'

In Mir's verse is a story; in Ghalib's is a totality. The same theme, Jalal Lakhnavi has expressed at a lower level:

be-nishaa;N hone me;N the apne tumhaare shuhre
tum mi;Taate hame;N ham naam tumhaaraa karte

[in our being trace-less was your fame
you erase us, we make your name]

But in the first line, the 'seating' of the words is fine.

In the present verse of Mir's too, the first line can be read in three ways:

1) beautiful ones, because of this wrecked heart of ours, are famous in the city

2) oh beautiful ones, because of this wrecked heart of ours, you are famous in the city

3) we, because of this wrecked heart of ours, are famous in the city of beautiful ones

FWP:

SETS == IZAFAT
MOTIFS == HOME; SCRIPT EFFECTS
NAMES
TERMS

The first line makes excellent use of its two possible, but not compulsory, izafat constructions:

mashhuur-e shahr ;xuubaa;N , 'famous in the city [are] beloveds'

mashhuur-e shahr-e ;xuubaa;N , 'famous in the city of beloveds'

mashhuur shahr-e ;xuubaa;N , 'famous [is] the city of beloveds'

The first reading is the most obvious; the second is also cited by SRF. The third reading is grammatically as possible as the others. (For semantic reasons, the line basically can't be read with no izafat.)

The deceptive quality of mashhuur and shahr is also enjoyable. The two are juxtaposed, so that we're invited to notice that they sound, and look in their spelling, as though they should come from the same three-letter Arabic root. But in fact they don't: mashhuur is Arabic and is indeed derived from the root shahr meaning 'to make conspicuous or notorious' (Platts p.1040). But shahr meaning 'city' is Persian, and is ultimately derived from a cognate of the Sanskrit kshetra , 'field' (Platts p.738).

The first line is full of such grammar games and word games, while the second line is arranged for contrast: radical simplicity, mostly short Indic words, no attempt at cleverness. Thus the effect of stark sincerity and unadorned suffering is all the more poignant.