Can a woman stay alone in Saudi Arabia for work in hospital (doctor) according to Shari'a?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Islam protects woman, maintains her honor and chastity and honors her as a daughter, sister, mother and grandmother. Islam also imposes on her guardian to take care of her and to provide her with food, clothes and all other essential needs.
At the same time, Islam permits her to work and manage her own affairs, but within precepts and standards of Shari'a. Thus, she is not permitted to travel alone, i.e. without a Mahram (unmarriageable person).
It is recorded by al-Bukhari and Muslim from Ibn 'Abbas (Radiya Allahu Anhu) who said: 'I heard Allah's Messenger (Sallallahu Alaihi wa Sallam) say: "No one should be alone with a woman except with a Mahram, no woman should travel except with a Mahram". A man got up and said: 'O Allah's Messenger' my wife will go to perform Hajj (i.e. this year) and I am enrolled in the Ghazwa (military expedition led by the Prophet (Sallallahu Alaihi wa Sallam) of so and so'. The Prophet (Sallallahu Alaihi wa Sallam) said: "Go off and perform Hajj with your wife" .
The above-stated Hadith indicates illegality of woman's traveling alone, and it is obligatory for her to be accompanied with a Mahram from her family, since it is possible for a traveler to face difficulty and fear.
On the other hand, according to the opinion of some scholars, a woman is permitted to travel (without a Mahram) as long as there is trusty company with her. This opinion is based on a Hadith reported by Khabab Ibn al-Arat that Allah's Messenger (Sallallahu Alaihi wa Sallam) "Gave them good news of spreading of Islam so that a woman (i.e. mounting a camel, …) can travel (alone) from San'a to Hadramout (a far place in the east of Yemen)" . [Reported by Imam al-Bukhari ].
This group of scholars, i.e. the minority of scholars, believe that the cause for preventing a woman from traveling alone is "absence of security and fear". So, if such a state vanishes, the ruling ceases to exist and it becomes normal for a woman to travel alone, which is subject to the rule of legality of travel in general.
Thereupon, if the sister inquirer lives in safe and secure place and with reliable company, then there is no objection to continue in her work; and if she wants to travel even to her own country, she has be accompanied by her husband or a Mahram.
Allah knows best.