In 1921, the short-lived parliament of Southern Ireland had its first and only election. The results, were a blowout for Sinn Fein, who won all but 4 seats (with those four seats being appointed by Trinity College Dublin). Sinn Fein boycotted the new parliament, formed their own and Southern Ireland as an entity ceased to exist after that.
What I'm wondering, however, is how Sinn Fein not only won 100% of the contested seats in 1921 but won them all by default. Not a single unionist stood for election in any of those 124 seats, even though they had an overpowering presence in the simultaneous Northern Irish Elections. Outside of Ulster, they'd won 1/3 of the votes in the seats they stood in during the 1918 General Election so there must have been *some* unionist presence outside of Ulster. What is the reason attributed for not a single unionist, from any party, even competing for one of the 124 Southern Irish seats in 1921?
I haven't found a single explanation online about this and the one JSTOR article I found was paywalled. Wikipedia makes a reference to a single Unionist MP claiming their parties were too scared to run, fearing retribution from Sinn Fein, but I'd like to see other sources back such claims.
Tl;DR: Unionists in the Irish Free State remained politically absent because they feared retribution. Events between 1919 and 1924 reinforced this. Unionists existed still but their politics were eventually subsumed into Irish conservatisim.
I'm going to couch this as the story of two James Craigs and suggest that the story of the 1921 Irish Election was really a small proxy political contest that was part of the greater Unionist/Nationalist "cold war" that had lingered since 1912. To get to our two Craigs, however, I've got to, unfortunately, dismantle your question a little.
Did no Unionist stand in the election for the Southern Ireland Parliament (Mansion House)? No. Four were elected and a fifth* bowed out of the contest late. Then again, no seat was actually contested on election day for Mansion House (but the Northern Ireland Election (for City Hall**) appears to have run mostly smoothly).**
What you're missing in your question is the correct number of seats in Mansion House prior to the boycott and establishment of the Second Dáil. There were actually 128 members elected to the ill-fated Mansion House parliament. Following Westminister tradition Dublin University (really Trinity College, but that's a story for another time) elected its own represenatives. These four men were Prof. Ernest Alton, Gerald Fitzgibbon, Prof. William Thirft, and, of course, James Craig.
Now, I could see someone arguing that these were "no true Irishmen" particularly if they claimed to be independent Unionists, but apart from Thrift they were all Irish born and bred. Alton and Fitzgibbon were from Westmeath and Dublin respectively. They even remained involved in Irish politics. Alton was elected to the third Dáil and won the next five elections before becoming a seantor untile retiring in 1943. Fitzgibbon was appointed a judge to the Supreme Court and had a hand in the creation of Artilce 26 of the 1937 constitution. Additioanlly, James Craig was also elected at the Third Dáil and relected five more times before his death in 1933.
Researching this answer I was absolutely struck by the chance existence of two James Criags from similar socio-political backgrounds (well off Anglo-Protestants) but with such differing results. Professor James Craig was born near Bushmills, Co. Antrim in 1861. He was 10 years senior of Sir James Craig, Viscount Craigavon, Prime Minister of Northern Ireland (b. 1871, Sydenham, Belfast). Whereas Sir Craig sought a military career in South Africa, Prof Craig was an academic drawn to the medical school in Dublin. Perhaps in this lays the rub: Prof Craig lived through and witnessed more of the Southern context and the Northern and Imperial context that Sir Craig lived and insomuch they're a stand-in for the binary context of the last years of a unified Ireland.
Prof. Craig exemplifes the soft unionism that has been dissolved into the waters of conservative politics in the Republic of Ireland. Let's be clear, despite 1916, Unionism was still a very viable political ideology in Dublin. The modern view that Unionists must have been "West Brits" or actively Imperialist is utter bunkum: Unionism, as it was then, was simply a politically conservative ideology arising in opposition to Home Rule from the late nineteenth-century onwards. Many of Ireland's leading businesses were openly Unionist: Jacobs, Jameson, and Guiness were all Unionist businesses. After the 1918 Election, however, influential Unionists chose to abstain from the political process in much the same way some Nationalists did in the North. This abstentionism was exascerbated by conflict: Anglo-Protestants who saw themselves as Irish but loyal to the British crown focused their energies outside of the political sphere. The Irish War of Indpendence and, later, the Irish Civil War caused great fear in the Unionist community and led to violence. Sectarian killings of Protestants spiralled into the hundreds in the period of 1920-21 (Hart). They saw that republicanism held the day and that they were no longer of any real consequence: why contest an election you'll lose only to mark yourself a traitor? Eventually, many Unionist Protestants would either blend into the new politics of Ireland or leave to England or Belfast.
Sir Craig flew the fleg of nascent Loyalism; a further evolution of Unionist political thought made possible by the establishment of the Northern Irish state. The situation faced by nationalists in the North was worse. While they were mostly unmolested by the wars of the early 1920s the new administration in Belfast City Hall saw fit to cement a Protestant hegemony within the six counties by the derrogation of the rights of Catholics. You could argue that much of the politics of the North were in response to the happenings in the South, but that underplays the strange influence of Belfast politics on London. I mean, the power weilded by Belfast through its government shouldn't be overlooked as we do now: there was a Prime Minister of Northern Ireland (Sir James Craig) when there wasn't even a parliament in Edinburgh or Cardiff! Sir Craig and other proto-Loyalists bullied successive Westminister governments, threatening insurrection and coups, the Curragh Incident being a great example. Diarmaid Ferriter touches on the weird relationships between Craig and David Lloyd George (the latter either through laziness, expediency, or some defference to the former military figure promised anything Craig asked for). Unionism in Northern Ireland was such a politically unifying ideology that it intensified to the point where Loyalism, an extremist variant that sought the maintenance of connections with London by any means necessary, developed with Jimmy of Craigavon and Edward Carson (who strangely didn't warrant much of a mention in this answer).
Ultimately there were Unionists in Ireland during the time of the Second Dáil although many chose to remain politically aloof. Four of them were "elected" to the Mansion House parliament but they, in turn, boycotted the breakaway Dáil only for them all to be elected to the Third Dáil. Their Unionism was tempered through their experience of living through a period of fear, by baring witnessing violence and political reprisals (it didn't become the extreme Unionism found in Belfast City Hall and later Stormont). Their politics became part of the mainstream of Dublin life so much so that when Prof James Craig died in 1933 the President of the Dáil, Eamon de Valera said
Members of the Dáil will have learned with deep regret of the death of Deputy Sir James Craig, who represented the constituency of Dublin University. Until his health began to fail, Deputy Sir James Craig was constant in his attendance and assiduous in his attention to the work of the House. His keen interest in matters of public health and his work for the improvement of our hospital system demanded the respect of all his colleagues, while his relations with his fellow-Whips and his contribution to our debates were marked by unfailing courtesy. I ask you, a Chinn Comhairle, to convey to Lady Craig and her family an expression of the sympathy of the Dáil with them in their bereavement.
Could you ever imagine de Valera speaking so kindly of Sir James Craig? Alton, Fitzgibbon, Thirft, and even one James Craig were Unionist politicians who became fundamental parts of the establishment of the Republic of Ireland.
* Robert Moore from Coleraine, theologian and politician, associated with Queen's University Beflast ** Stormont didn't open until 1932 and this is wonderful symatery (Mansion House/City Hall). Queen's University Belfast also provided elected members for the Northern Irish Parliment
Peter Hart, "The Protestant Experience of Revolution in Southern Ireland", Patrick Maume, "Ulstermen of Letters", and Ian McBride, "Ulster and the British Problem", all have deeply fascinating essays, titles given, on this topic in Unionism in Modern Ireland: New Perspectives On Politics and Power ed Richard English and Graham Walker.
Royal College of Physicians, Ireland, Heritage Centre https://rcpi-live-cdn.s3.amazonaws.com/wp-content/uploads/2017/09/106-Sir-James-Craig.pdf
Quote from Eamon de Valera via the Oireachtias website https://www.oireachtas.ie/en/debates/debate/dail/1933-07-13/2/