If you survive your time imprisoned yes you will remain alive, most likely. A monarch, or even a simple noble, is a valuable spoil of war. You would most likely be ransomed for your release.

A monarch however will certainly be ransomed with a lot of concessions to make toward his victor. There are several examples I can think of, the most famous example that I know of his when King Francis I of France was made prisoner by Charles V, Holy Roman Emperor.

Once again, Francis played the impetuous and " over chivalrous " card and did not listen to his advisers ( though none of them agreed on what to do really ) at the Battle of Pavia in 1525. Francis was too confident and thought to enact again his victory at Marignan in 1515. He charged in the same old French knightly fashion ( pretty much like what he read in books ) which ended disastrous. Many are killed and Francis himself is wounded and has to give up his sword to the enemy. The King is made prisoner, taken from one place to another. Some records show that if he was not badly treated because of his value he was far from being well treated and fell ill ( which caused much fear to Charles V ). Francis would stay a bit less than a year as the Emperor's prisoners and the cost for his is great but necessary for the King's release ( whose Kingdom started to feel his absence ). Two duchies have to be given up to the Emperor, the French King had to give up all claim on Italian and Flemish territory and had to marry a sister of the Emperor. More importantly, he had to give two sons to the Emperor as " wards " ( who will not be treated very well and it will have a lot of consequences on the future Henri II's psychology and view of the Empire ). Also, the ransom was absolutely gigantic, something like 2 years of France's monetary gain.

Another example is Jean II " the Good " of France who was captured in 1356 at the disaster of Poitier. The King's Kingdom and subject saw him as a hero who sacrificed himself. King Jean had more luck than Francis in his captivity as he was treated very well by the English King Edward III. He was sent to Bordeaux, in English occupied territories and incarcerated there. However, he had a castle to his disposition ( without the right to leave of course ) and the possibility to have a court. King Jean had the possibility to keep working almost like he used too. However in his absence political turmoil was starting to grow and frighten the King who decided it was time to act. He was offered a treaty, very generous, known as the Treat of London 1358. From Bordeaux the king was transferred to London where he had his own house, own court and free passage in all of London. However, the others terms of the treaty were that England regained all its former possessions in Aquitaine. A quasi civil war began in France with the Parisian mayor taking control of the city. In 1359, King Jean was loosing his much of his power and influence in France which made the English monarch becoming more and more demanding and less ... nice. He demanded half the French territory and the equivalent of more than 5 years of yearly financial gain. In France, the Dauphin ( the heir ) took power and declared his father incapable to rule and not responsible of his actions during his captivity. The Dauphin took arms and lead the fight against England in a war of " quasi guerrilla " while raiders started to create a panic in England and a fear of an invasion. Edward III was furious to be loosing and his army, marching towards Paris became extremely violent against civilian population. This created a hatred towards the English and a popular empathy for the captured king. Jean the Good is sent to an English fortress and his conditions are nothing like they used to be. With the English army in total disarray, France managed to sign a new treaty in Bretigny. The cost is still high and in addition to territory loss, the ransom is equivalent to two years of financial gain to deliver in less than a year. Finally, after finding the money ( taxes but considering the state of France and the impossibility to ask more of the people that suffered so much of the war, he used money he gained in a quick marriage of his daughter ) Jean II is released.

So, as you saw in these two examples. A captured monarch is of immense value and worth keeping alive. In addition to a ransom, you have the possibility to make extreme demands over your prisoner. Funnily enough, King Jean the Good four years after his release willingly returned to English captivity after his hostage son Louis escaped. It also lead him to be quite popular with the people who feared English retaliation after the prince's escape but the king gave himself.

Sources : personal knowledge concerning Jean II as well as radio show and Le roi Jean II le Bon fut-il un mauvais roi ? in an edition of magazine Historama 2003 by the Duke of Levis Mirepoix. François 1er, roi de chimères Broché –2014 by Frank Ferrand