There were many frontiers - the term covers as large swath of time and geography, so giving a precise, generic, "fits-all" answer to your question is impossible. That said, the general pattern was for a predominance of men to arrive in an area followed by families. Because there were typically more men available in the general area, it was usually easy for an adult woman to link herself up with another man. In fact, her ilk - an unattached woman - was so rare that it would be difficult to resist all the efforts to pin her down. So she wouldn't have to survive long without the skills of a man.

On the other hand, women like all of humanity, could be enormously resourceful, so I wouldn't count out the possibility of a woman fending for herself and her family all alone, just as a man left with children because of the death of his wife could do what he could and needed to do to survive and care for children. One should never count out that possibility.

All of this sounds frighteningly close to the debate on the frontier spawned by Frederick Jackson Turner, and I don't mean to open up that old wound in western historiography. One should keep in mind, as said, that there were many frontiers. Often times - particularly in the Intermountain West - urban settlements arrived almost instantaneously, so families arrived in consort with a large number of single men. And again, an ample supply of single men meant that no woman would need to stay single longer than she wished.

I've been doing a great deal of research on women on the western frontier (specifically Montana, Wyoming, Colorado, and California) during 1840s-1919.

I want to preface my answer with the comment that women are pretty much capable of doing anything a man can, and can even do it while bleeding. Accounts on the overland trail describe women doing much the same work as men.

A woman would have an advantage in the western territories that she wouldn't back east- the ability of women to own land during this period was legislated in the Montana Territory. Due to the mining industry's boom and bust cycle, the men would pull up stakes and go to new work camps, often leaving the women and children behind. This was ultimately what led to women being able to own and defend (physically and legally) a homestead.

There was a huge difference in the number of women and men on the frontier. One woman described her experience of not being a particularly handsome woman, but having men come from miles around just to see a woman. My notes are at home (I will update later), but if i remember correctly in the earliest days of the frontier the ratio was 1 : 100, only decades later did it narrow to 1 : 3. So a large portion of women turned to prostitution. It was one of the most profitable and safest ways(if they worked in a brothel they often had housing, protection, access to healthcare) for a woman to survive on her own. A huge number of my sources have also mentioned women using prostitution to find a husband, sounds odd, but apparently many women married out of the profession.

This is not to say all women in the western frontier were prostitutes, but a great deal of them were. For a woman who found herself alone with a scarce commodity for sale, she most definitely could have made a living or replaced a spouse very easily.

Cole, Judith K. “A Wide Field for Usefulness: Women’s Civil Status and the Evolution of Women’s Suffrage on the Montana Frontier, 1864-1914.” The American Journal of Legal History, Vol. XXXIV. 262-294.

Larson, Sharon L. “Wyoming Gives Women the Vote.” Salem Press Encyclopedia, January, 2015.

An Illustrated History of Prostitution

Madeleine: An Autobiography. New York: Harper & Brothers, 1919.

Bullough, Vern L., and Bonnie Bullough. 1978. Prostitution : an illustrated social history. n.p.: New York : Crown Publishers, c1978.

To give you further insight into one small slice of the almost-frontier, I can shed some light on some of the practices that occurred in late territorial Missouri/ early territorial Arkansas, specifically early Lawrence County. As u/itsallfolklore has stated, it was common for people living in the area to remarry. What might happen before that remarriage, if it happened at all, often depended on the last will and testament of the deceased. As one example, David Lister of Davidsonville Arkansas passed away March 2nd, 1818. In the probate collection of the Northeast Regional Arkansas Regional Archive, his last will and testament appoints his business partner (and mentor) Adam Ritchey as the executor of his estate. Lister requested that Ritchey ensure that his family is provided for in every respect. The document folder behind the will contains roughly two dozen receipts filed by Ritchey, listing money withdrawn from the estate for clothing and other household essentials for the care of the Lister family.

This type of care could go further than just financial provisions. The last will and testament of one John Reaves(died September 6th, 1827) also of Davidsonville Arkansas appointed a neighbor by the name of Casper Schnuck as administer of his estate. Schnuck was appointed to look after Reaves’ wife Patience and daughter Nancy. In addition to the usual financial matters, Schnuck was also charged to look after Nancy and foster her if Patience was not properly looking to her child’s well-being. The documents don’t say whether the charge given to Schnuck to, “either marry her, or otherwise to put her into a good house until she is grown” was ever carried out, but seem to indicate that this particular husband wasn’t sure that his wife could care for their daughter on her own.

Conversely there were other women in the county whose husbands left them full control of significant portions of property and other wealth. When John Tyler Jr of Lawrence County passed away, he left “the whole of his property after his just debts were paid to his beloved wife Pally Tyler for the use of her family.” Mrs. Tyler was lucky in that she (among others) had wealth to be deeded to her. Dr. J. B. Perkins in his work, Women and American Settlement in Territorial Lawrence County relates several other cases from court records where widows were so poor that they were designated paupers and given a sum to live off of in an early form of welfare.

To sum up, in this little corner of the country that was quickly leaving frontier status, what women had to contend with and do to survive depended on a number of variables. Wealth of the family pre-widowing was a key issue, along with the relationship the couple had had. Remarriage, foster care, and going it alone were all viable options for women and their families and each had their potential perils and pitfalls.

Sources:

David Lister Probate Records, 1818, LCHS Probate Box 17, Folder 1289

John Reaves Probate Records, 1827, LCHS Probate Box 23, Folder 1779

Perkins, J. Blake. "Women and American Settlement in Territorial Lawrence County." The Arkansas Historical Quarterly 75, no. 2 (2016): 111.

You should read 'Women of the Frontier' by Brandon Marie Miller (978-1883052973). Each chapter follows one woman's story. Some parts I wished were more nuanced, but it gives an inside look at life on the Frontier for women. Many of the women were separated or lost their husbands. Overall, a quick, but informative and entertaining read.

(On mobile, sorry for formatting.)

Follow-up question: Was prostitution prevalent in that place and era?

The autobiography and illustrated history I mention above both make reference. The illustrated history also has images of tokens that were used in place of money so women couldn't skim off the top at "boarding houses."