OK. Throughout the series Kagura and Sesshoumaru "happen" to run into eachother. One instince was when she was run through the chest and fell into a river to drawn. Rin saw her body floating along with the currant and jumped in to save her, grabbing Jaken to help too. Sesshoumaru watches and eventually jumps in to save them. Mind you, Sesshoumaru has one arm so grabbing to small frames and a grown woman's frame is a bit tricky with one arm. Meaning, he had to have wanted to save her because he could have easily just saved Rin and Jaken without a problem. But he saves her too. (she doesn't have a top either it got ripped up XD) Anywho.
Also everytime the run into each other the distance gap between them gets smaller.
*SAD PART OF THE SPOILER*
Kagura has crossed Naraku for the last time, and he gives her heart to her, poisoned with miasma, telling her she is finally free, but she only has enough time to enjoy it in horrendous pain. Sesshoumaru smells Naraku's blood and miasma and goes off towards it. So away he goes. After fighting Mouryoumaru again, Kagome convinces Kohaku to stay with them and Sango. Inuyasha smells Kagura's blood. Everyone is freaked and they run off to her direction.
Kagura is happy that she can feel her heart beat and wonders where she should go, but realizes that she is dying. Sitting in a field of flowers she is sad thinking that she will die alone and thinks that this was the freedom she was seeking. Suddenly Sesshoumaru walks up to her and Kagura is surprised. He tells her that he followed the scent of Naraku's miasma. She laughs and asks him if he was dissapointed that she wasn't Naraku. He tells her that he knew it was her. She's surprised again. He takes out the Tenseiga, but disturbed that it can't save her. She smiles at him as Inuyasha and co come to them. Kagura turns into dust into a gust of wind and blows away. Inuyasha asks Sesshoumaru if she was suffering and he tells her she was smiling. They look up at a single white feather drifting in the wind.