The easiest way for this to happen is for one party to become so ideologically extreme that it alienates all but its most ardent members, while the other party becomes an absolute unit of a big tent. Eventually the extreme party becomes a minor party in a Singapore-ish basically-one-party system.
Most likely this would result in a split of the megabigtent party into two or more parties, as it would no longer have a common enemy to keep it united.
I suppose the most plausible way for this to happen in modern America would be a Republican base that refuses to let go of Trumpism and a Democratic Party that abandons any specific ideology in favor of becoming the "anything but Trumpism" party, resulting in the Democratic big tent expanding to the maximum (somewhere around 67% of the country, based on polls on specific issues showing that about 1/3 are true "deplorables") and eventually splitting, presumably into moderate and progressive parties.
Could we have a "Democracy" with a one party system?
A one-party system is as democratic as the party wants it to be. So, yes, but it would be fragile.
