Settings People: Prevent long profile names from clobbering buttons.

chrome/browser/resources/settings/people_page/people_page.html

 <link rel="import" href="chrome://resources/cr_elements/icons.html">
 <link rel="import" href="chrome://resources/html/i18n_behavior.html">
 <link rel="import" href="chrome://resources/html/icon.html">
 <link rel="import" href="chrome://resources/html/polymer.html">
 <link rel="import" href="chrome://resources/html/web_ui_listener_behavior.html">
 <link rel="import" href="chrome://resources/polymer/v1_0/neon-animation/neon-animatable.html">
 <link rel="import" href="chrome://resources/polymer/v1_0/paper-button/paper-button.html">
 <link rel="import" href="chrome://resources/polymer/v1_0/paper-checkbox/paper-checkbox.html">
 <link rel="import" href="chrome://resources/cr_elements/cr_dialog/cr_dialog.html">
 <link rel="import" href="/controls/settings_checkbox.html">
@@ skipping 23 matching lines @@
       setting-box.middle {
         /* Per spec, middle text is indented 20px in this section. */
         -webkit-margin-start: 20px;
       }
 
       #profile-icon {
         background-position: center;
         background-repeat: no-repeat;
         background-size: cover;
         border-radius: 20px;
+        flex-shrink: 0;
         height: 40px;
         width: 40px;
       }
 
       #managed-by-domain-name {
         font-weight: bold;
       }
 
       iron-icon[icon='settings:sync-problem'] {
        --iron-icon-fill-color: var(--settings-error-color);
@@ skipping 263 matching lines @@
 
 <if expr="chromeos">
     <template is="dom-if" if="[[easyUnlockEnabled_]]">
       <easy-unlock-turn-off-dialog id="easyUnlockTurnOffDialog">
       </easy-unlock-turn-off-dialog>
     </template>
 </if>
   </template>
   <script src="people_page.js"></script>
 </dom-module>