Directly this will not work hence we will need to remove AutoPostback from TextBox and add a Fake LinkButton to make it work
HTML
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<title></title>
<script type="text/javascript">
function Validate(o) {
if (o.value != "") {
__doPostBack(o.name, "");
}
}
</script>
</head>
<body>
<form id="form1" runat="server">
<asp:TextBox ID="TextBox1" runat="server" OnTextChanged = "TextChanged" onblur = "Validate(this)"></asp:TextBox>
<asp:LinkButton ID = "fake" runat = "server"></asp:LinkButton>
</form>
</body>
</html>
C#
protected void TextChanged(object sender, EventArgs e)
{
Response.Write("Your entered:" + TextBox1.Text);
}