.container {
    display: -webkit-flex;
}

div {
    white-space: nowrap;
    text-overflow: ellipsis;
}

.container > div:last-child {
    -webkit-flex: 1;
    background: red;
}

<!-- a small first column; the second column is taking up space as expected -->
<div class="container">
    <div>foo barfoo bar</div>
    <div>foo bar</div>
</div>

<!-- a large first column; the first column is overflowing out of the flexbox container -->
<div class="container">
    <div>foo barfoo barfoo barfoo barfoo barfoo barfoo bar
    foo barfoo barfoo barfoo barfoo barfoo barfoo bar
    foo barfoo barfoo barfoo barfoo barfoo barfoo bar</div>
    <div>foo bar</div>
</div>

.container {
    display: -webkit-flex; 
}

.container>div:first-child{
    white-space:nowrap;
   -webkit-order:1;
   -webkit-flex: 0 1 auto; /*important*/
    text-overflow: ellipsis;
    overflow:hidden;
    min-width:0; /* new algorithm overrides the width calculation */
}

.container > div:last-child {
    -webkit-flex: 1;
    -webkit-order:2;
    background: red;
    -webkit-flex:1 0 auto; /*important*/
}
.container > div:first-child:hover{
    white-space:normal;
}

<div class="container">
    <div>foo barfoo bar</div>
    <div>foo bar</div>
</div>

<div class="container">
        <div>foo barfoo barfoo barfoo barfoo barfoo barfoo bar
        foo barfoo barfoo barfoo barfoo barfoo barfoo bar
        foo barfoo barfoo barfoo barfoo barfoo barfoo bar</div>
    <div>foo bar</div>
</div>
<div class="container">
    <div>foo barfoo bar</div>
    <div>foo bar</div>
</div>

<div class="container">
        <div>foo barfoo barfoo barfoo barfoo barfoo barfoo bar
        foo barfoo barfoo barfoo barfoo barfoo barfoo bar
        foo barfoo barfoo barfoo barfoo barfoo barfoo bar</div>
    <div>foo bar</div>
</div><div class="container">
    <div>foo barfoo bar</div>
    <div>foo bar</div>
</div>