House-shaped [Edit 3]

[Akira]

It is a style choice you are certainly not incorrect in making, but I would consider not Capitalizing every line-- it's an older style and tends to suggest you are following some formal form, like a sonnet, which you are not.

We shape our buildings, and thereafter they shape us.  - Winston Churchill, 1944

A home is not a trap, a house may be:    This is a nice opening, but I am not sure if you explore it -- You describe how "home-ness" is lost, but I don't really see the trap.
The home may form, break - all depends upon
Each person who arrives, abides, departs,
Who loves or hates, who dies or procreates.
Each one shapes home-life - but the house endures.

The single man who buys a house invests -
Depreciation’s his alone to bear;   Pet peeve, but Depreciation's bothers me, would prefer to see it without the "'s" or spelled out
Appreciation swells his sole net worth.
But if he never marries, fails to form
A family, his house fills with the dust
Of years, possessions, everything but trust  I wonder if you need this, or could just end on "fills with dust." then "He's shaped..." I think the dust standing for those types of things is inferable from what precedes.
In others.  He’s shaped by its walls, constrained;
His house is comfortable, so is he.
But should he, childless, try to break its chains,
Each book, each chair and etching forms a link
That binds him, owned by all the things he’s bought.

As sad or sadder is the fate of those  "or sadder" is a needlessly distracting call for the reader to make a comparison that isn't the point of the poem.
Whose family disintegrates but leaves
Their house of many years, once home, a prize
To be fought over.  All its joy escapes   By saying "Their house, once home" you've set it as after the fact, so perhaps "All joy escaped like..." (past tense)
Like baby’s breath; too soon there’s nothing left  
But walls and cellars, plumbing, attic, floors
Its former residents each claim to own.

We shape our houses, Churchill said, but then
They mold us.  If the cast is too exact,
Too hard, we cannot leave until we melt -
For we’re no longer shaped to pass their doors.

Beyond the above, I think the language is still a touch, hmm, not sure how to describe -- formal, stilted? -- I think this could be tightened further and you would't lose what you think you would.