Liquidity is a property not of the money but of the market around it. USDT is liquid: it is accepted everywhere and in any volume. An obscure token may be worth anything on paper, yet selling it at that price will not work.
How you notice it when exchanging
In the reserve for a direction. The reserve is the funds a service holds right now; an order larger than the reserve will not be filled immediately, even if a rate is displayed.
And in the rate differing by amount. If a service quotes one rate for a hundred dollars and another for ten thousand, that difference is the price of liquidity.
Why rare directions have worse rates
Exchanging USDT for hryvnia is simple: thousands of people buy both every day. Exchanging an obscure token for zloty is a task where the other side has to be found, and the cost of that search goes into the rate.
What to do with a large amount
Split it up or give notice in advance. An order noticeably larger than a direction's usual turnover takes longer to fill, not because it is being scrutinised but because the matching volume is being gathered for it.
Giving notice removes that delay entirely: the service has time to prepare and the exchange runs at its usual pace.