The series is Nasa's Dying Dream.
A little obvious, but Nasa getting hit by a truck would mean that his injuries would have been more grievous than what was presented. As he laid dying, Nasa is distraught by the fact that his life was going to end abruptly. Tsukasa suddenly coming out of nowhere to save Nasa could mean that she is perhaps the Angel of Death come to collect Nasa's soul and carry him over. Their "marriage" is really her giving Nasa everything that he wanted before he flatlined. Tsukasa is a Reaper from Dead Like Me
Specifically, from the Plague Division. She talks about things in history as if she was actually there, comments made about her imply she doesn't age, and injuries that would kill a normal person are simply walked off and heal rapidly (i.e. during the anime, the trail of blood she leaves simply ends without showing signs of having slowed). The real reason why Tsukasa proposes marriage to Nasa.
From her interaction with her family, its implied that she wanted to experience living as a commoner and prefers to get away from her clingy adopted sister Chitose as far as possible. While Nasa only asked to date her, Tsukasa goes as far as to propose a marriage may come from the fact that she is a Single Woman Seeks Good Man as well. Tsukasa is not Princess Kaguya.
Rather, her true identity is that she was one of the people who lived during Princess Kaguya's arrival to Earth. When Kaguya returned to the Moon, she left the emperor her elixir of immortality which he sent it to burn at the Mount Fuji as he rejected the idea of immortality. Tsukasa actually administered one of these exhibits and lived a very long life as a 16 years old teenager, meeting Tokiko and eventually adopted under that woman's name. She has a lot of lovers and Nasa just happens to be her recent one, which she gladly took advantage by offering to marry him. In addition, Tsukasa's ability to tank an incoming truck was due to her immortality from the elixir.- Relating to above, Kaguya Gekkou might be the true Princess Kaguya, who's arrival to Earth is due to Tsukasa's use of the elixir of immortality.
- Partially confirmed: chapter 147 confirmed Tsukasa is the daughter of Iwakasa, the man the Emperor gave the immortality elixir to, with orders to burn it on the tallest mountain. Tsukasa however, was ill and dying, so he chose to give the potion to her instead. But she has not had any lovers, her first kiss with Nasa was her first kiss ever. Also, she's not 1416 years old. She's had 1400 16th birthdays.
Tsukasa's wish will be fulfilled not by undoing her immortality, but instead giving immortality to Nasa thus ending her loneliness forever.
The series is sprinkled with very subtle hints pointing towards this. Possibly Tokiko never actually wanted to help Tsukasa become mortal again, but rather to give her an eternal companion, so she has a reason to live on, without ever having to face the eternity of loneliness again. Especially the dialogue from bonus chapter 140.5 strongly suggests this to be the case. Nasa and Tsukasa's exchange might just sound like some random flirting, but if you read it with the assumption that Nasa is also immortal at that point, then the conversation still perfectly fits and suddenly has a different meaning.