They really can't sell their slaves in the antebellum South. They need x number of slaves to run their plantations so they can pay back their creditors and do all the things a Southern aristocrat is expected. Their slaves are collateral on their mortgages, so they can't afford to liquidate them.
Nonsense. Slaves could be, and were, sold in large numbers. Yes, in some cases, some slaveowners resisted selling their slaves... right up until the point said slaveowners went broke and all of their slaves were sold off to the highest bidder. The effect was the same in terms of mobility of slave labour.
Slaves were also rented out for industrial or other purposes, in some cases, even where not sold outright.
Because of these factors, slaves are very much tied to the land, and it hinders maximizing returns. Trying to get out of plantation production was both socially and economically difficult.
Slaves were
not tied to particular crops, to particular land, or even land in general. The economic history of the South makes that perfectly clear. When agricultural prices dropped - which they did most notably in the 1830s/early 1840s - slave labour moved out of agricultural plantations and into either urban centres, or sometimes into rural/small town industries (most notably textiles).
For details of movement of slaves in and out of cities in response to agricultural prices, see Claudia Goldin (1976) "Urban Slavery in the American South, 1820-1860".
For more general treatment of slave labour, its mobility between crops, or between geographical locations (i.e. not fixed to a given piece of land) see Gavin Wright, "Old South, New South" and "Slavery and American Economic Development" and Robert Fogel "Without Consent or Contract".
Historically, there weren't great movements of slaves from plantations to cities.
Not in times when agricultural prices are high, but that's because there was a limited supply of slaves, and the cotton planters could bid more for them.
When agricultural prices dropped, then slaves did move into the cities. Although many moved out again after cotton prices rose.
There were, however, massive movements of free labor to cities and industrial production, with the added benefit that free laborer could at least be working towards his own benefit, however meager that turned out to be.
In North American terms, that was true, but due almost entirely to immigration. During the early stages of North American industrialisation, the labour force consisted largely of immigrants, and in some cases native-born females (mostly the unmarried ones), since female labour was largely under-utilised, for obvious reasons.
Native-born American whites, especially American white males, were very resistant to working in early factories and the like. They were more inclined to work for themselves or try to strike out west in search of land and an independent lifestyle. Working for someone else was loathed, whether as a factory worker or as a hired hand on someone else's farm.
As I mentioned upthread, the presence of slavery (and, to a lesser degree the hostile disease environment) meant that immigrants mostly avoided the South. So whatever early industry developed there had to come from native labour, free or slave. Mostly slave.