From what I have read as molecular clouds are the birth place of stars, their population as you would assume are young stars or stellar remnants but so far I have not found out if there are main-sequence stars of the age of ours or older that have either wandered into a molecular cloud or are positioned close by.
I was wondering if we have observed any solar systems similar to the age of ours or older within or close to molecular clouds?
Stars do not stay where they are born. They orbit in our galaxy and their orbits are subject to relative perturbing forces caused by galactic tides and encounters with spiral density waves and other giant molecular clouds. A typical velocity dispersion for stars in the solar neighbourhood is $\sim 20$ km/s (or about 20 pc per million years). Thus once stars are billions of years old, they can have moved relative to the stars they were born with by a distance of order the size of the Milky Way.
Thus the positions of old stars are essentially randomised$^1$ and their density (near the Sun) is of order 0.1 per cubic parsec (including stars of all masses greater than about 0.1 solar masses - the smaller ones are much more numerous).
A typical giant molecular cloud in the earliest stages of star formation might be of order 10-100 pc in diameter, with a volume of 500 to 500000 cubic parsecs. You would thus expect about 50-50000 normal stars to exist within the boundaries of a giant molecular cloud of this size, simply at random. Note that a molecular cloud is far too sparse to offer any mechanical resistance to the motion of a star into it or through it.
Simply scale to the size you have in mind for your molecular cloud to get a different answer.
If you restrict the stellar types to say 0.8-1.2 solar masses, then you can reduce this number by about a factor of 10. If you restrict it to stars older than 4.5 billion years, then you could reduce the numbers by a further factor of 2-3, since the rate of star formation has been approximately constant for the last 10 billion years and this is comparable to the main sequence lifetime of a 1 solar-mass star.
$^1$ Note that there is a tendency for stars to oscillate around a mean relative position in an orbit (an epicycle) rather than wander randomly through the galaxy, but it still has the effect of smoothly randomising their relative positions.
A molecular cloud is a cloud of hydrogen and other molecules in space.
You may have noticed that in the atmosphere of Earth there are many clouds of dust and water vapor, and that solid objects like birds and airplanes pass thorugh those clouds with ease.
Molecular clouds are dense compared to most regions of interstellar space, but they are very thin vacuums compared to the clouds in Earth's atmospthere. They have no ability to bounce away a solid object which reaches their boundries. Instead the solid object will pass right through the molecular cloud.
A solid object passing thorugh a molecular cloud will sweep up some of the molecules near its path, creating a tunnel of even thinner vacuum through the cloud. Its gravitational and/or magnetic interactions with molecules it passes might change their paths through space and cause thinner and denser regions to form in the cloud.
The stellar density is the number of stars per unit of volume of space.
In the solar neighborhood, this value can be determined from surveys of nearby stars, combined with estimates of the number of faint stars that may have been missed. The true stellar density near the Sun is estimated as 0.004 stars per cubic light year, or 0.14 stars pc−3. When combined with estimates of the stellar masses, this yields a mass density estimate of 4×10−24 g/cm3 or 0.059 solar masses per cubic parsec. The density estimate varies across space, with the density decreasing rapidly in the direction out of the galactic plane.1
https://en.wikipedia.org/wiki/Stellar_density
If you calculate the volume of a molecular cloud in cubic light years or cubic parsecs, you can calculate the average number of stars which can be expected to be within that volume of space. And if you estimate or choose the volume of space which you count as being near a molecular cloud, you can calculate the average number of stars which would be near the molecular cloud at any one time.
At any one time a molecular cloud might contain one or more stars which are forming or have already formed, but have not yet dispersed. And a large enough molecular cloud will have a large enough volume that it will be statistically probable that one or more older stars that did not form in that molecular cloud will be passing though the cloud at any one time.
